Article
Physics, Multidisciplinary
Asela Abeya, Barbara Prinari, Gino Biondini, Panos G. Kevrekidis
Summary: The article investigates soliton solutions and interactions in a system of coupled nonlinear Schrodinger equations modeling the dynamics in one-dimensional repulsive Bose-Einstein condensates. Multi-soliton solutions are compactly represented using the Inverse Scattering Transform. The study includes a detailed characterization of canonical and non-canonical forms of solutions, as well as the classification of one-soliton solutions and their relationships to spectral data in the Inverse Scattering Transform.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Mathematics, Applied
Nan Liu, Jia-Dong Yu
Summary: The inverse scattering transform approach is applied to investigate the derivative nonlinear Schrodinger equation with nonzero boundary conditions and triple zeros of analytical scattering coefficients. A matrix Riemann-Hilbert problem associated with the equation is constructed based on the analytical, symmetric, and asymptotic properties of eigenfunctions. The reconstruction formula for the potential is obtained by solving the Riemann-Hilbert problem. The explicit expression of the reflectionless potential with triple poles for the nonzero boundary conditions is derived using determinants.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Engineering, Mechanical
Yehui Huang, Jingjing Di, Yuqin Yao
Summary: The defocusing Hirota equation with nonzero boundary condition is studied using the partial derivative-dressing method. A partial derivative-problem with non-canonical normalization conditions is introduced. The Lax pair of the defocusing Hirota equation with nonzero boundary condition is derived using an asymptotic expansion method. N-soliton solutions are constructed under a selected special spectral transformation matrix, and the dynamic behavior of soliton solutions is analyzed.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Junyi Zhu, Xueling Jiang, Xueru Wang
Summary: The Dbar dressing method is expanded to study the focusing/defocusing nonlinear Schrodinger (NLS) equation with nonzero boundary condition. A special type of complex function is considered, which is meromorphic outside an annulus with center 0 and satisfies a local Dbar problem inside the annulus. The theory of such function is extended to construct the Lax pair of the NLS equation with nonzero boundary condition. In this procedure, the relation between the NLS potential and the solution of the Dbar problem is established. A certain distribution for the Dbar problem is introduced to obtain the focusing/defocusing NLS equation and the conservation laws.
ANALYSIS AND MATHEMATICAL PHYSICS
(2023)
Article
Physics, Mathematical
Wei-Qi Peng, Yong Chen
Summary: In this work, the double and triple pole soliton solutions for the Gerdjikov-Ivanov type of the derivative nonlinear Schrodinger equation with zero boundary conditions (ZBCs) and nonzero boundary conditions (NZBCs) are studied via the Riemann-Hilbert (RH) method. The RH problem (RHP) is constructed based on the analyticity, symmetry, and asymptotic behavior of the Jost function and scattering matrix under ZBCs and NZBCs. The general precise formulas of N-double and N-triple pole solutions corresponding to ZBCs and NZBCs are derived, and the dynamical behaviors for these solutions are discussed.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Jin-Jin Mao, Shou-Fu Tian, Tian-Zhou Xu, Lin-Fei Shi
Summary: This paper studies the inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrodinger equation with different boundary conditions. Bound-state soliton solutions with zero boundary conditions are derived for the first time using the residue theorem and Laurent's series. The Riemann-Hilbert problem for the inhomogeneous fifth-order nonlinear Schrodinger equation with nonzero boundary conditions is revealed by combining with the robust inverse scattering transform. Moreover, new rogue wave solutions are found using the Darboux transformation based on the resulting Riemann-Hilbert problem. The unreported dynamic characteristics of the corresponding solutions are further analyzed and displayed through selected graphs.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2022)
Article
Mathematics, Applied
K. T. Gruner
Summary: Soliton solutions for the nonlinear Schrodinger equation on two half-lines connected via integrable defect conditions are reconsidered using the dressing method. N-soliton solutions are explicitly constructed and it is shown that the solitons are transmitted through the defect independently of one another.
Article
Mathematics, Applied
Guixian Wang, Bo Han
Summary: In this work, the discrete modified Korteweg-de Vries equation under nonzero boundary conditions is studied using the robust inverse scattering transform. The Jost solutions, scattering matrix, and their properties are presented based on the Lax pair. Riemann-Hilbert problems and Darboux matrix are constructed using the robust inverse scattering transform, and rational solutions are deduced with detailed graphical characteristics exhibited by choosing suitable parameters. The results are useful for explaining related nonlinear wave phenomena.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Nan Liu, Zuxing Xuan, Jinyi Sun
Summary: The triple-pole soliton solutions to the classical DNLS equation with zero boundary conditions at infinity are constructed using the inverse scattering transform method. Detailed analysis of the discrete spectrum in the direct problem is presented under the condition of the scattering coefficient having N-triple zeros. The general solution of the DNLS equation and an explicit N-triple-poles soliton formula for the reflectionless potential are obtained through the matrix Riemann-Hilbert problem with triple poles.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Optics
Yan-Hong Qin, Liming Ling, Li-Chen Zhao
Summary: The spatial-temporal patterns of rogue waves in N-component coupled defocusing nonlinear Schrodinger equations are investigated in this study. The correspondence between modulation instability and rogue-wave patterns is established, enabling the prediction and control of different rogue-wave modes.
Article
Engineering, Mechanical
Yu Xiao, Qiaozhen Zhu, Xing Wu
Summary: This paper presents the inverse scattering transform (IST) with Riemann-Hilbert problem (RHP) for a higher-order extended modified Korteweg-de Vries (emKdV) equation with zero/nonzero boundary conditions (Z/NZBC) at infinity. The research results show the formulas for multiple simple poles soliton and higher-order poles solution, as well as the detailed effect of the variable values of the third- and fifth-order dispersion coefficients on the dynamic structures.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Asela Abeya, Gino Biondini, Barbara Prinari
Summary: This paper develops the inverse scattering transform (IST) for the defocusing Manakov system with non-zero boundary conditions at infinity, involving non-parallel asymptotic polarization vectors. A uniformization variable is used to eliminate the square root branching, and the adjoint Lax pair is applied to overcome the non-analyticity problem of some Jost eigenfunctions. The inverse problem is formulated as a matrix Riemann-Hilbert problem (RHP), and methods for converting the RHP into linear algebraic-integral equations are presented.
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Xiu-Bin Wang, Bo Han
Summary: In this study, we systematically investigate the inverse scattering transform of the general fifth-order nonlinear Schrodinger equation with nonzero boundary conditions. We find a simplified form of the equation by reducing it to several integrable equations, and construct the general solutions for reflectionless potentials. We also analyze the dynamics of the obtained solutions in terms of their plots.
THEORETICAL AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
Summary: The Riemann-Hilbert problem is developed to study the focusing behavior of the nonlinear Schrodinger equation with multiple high-order poles. By employing Laurent expansion and solving an algebraic system, soliton solutions corresponding to the transmission coefficient are obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematics, Applied
Vincent Caudrelier, Nicolas Crampe, Carlos Mbala Dibaya
Summary: This study analyzes the focusing nonlinear Schrodinger equation on the half-line with time-dependent boundary conditions using Backlund transformations and nonlinear method of images. Two possible classes of solutions are identified, one similar to Robin boundary conditions where solitons are reflected at the boundary, and a new regime where one soliton can either be absorbed or emitted by the boundary. The unique feature of time-dependent integrable boundary conditions is demonstrated.
STUDIES IN APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Alyssa K. Ortiz, Barbara Prinari
STUDIES IN APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Georgios N. Koutsokostas, Theodoros P. Horikis, Dimitrios J. Frantzeskakis, Barbara Prinari, Gino Biondini
STUDIES IN APPLIED MATHEMATICS
(2020)
Article
Physics, Multidisciplinary
Aikaterini Gkogkou, Barbara Prinari
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
Article
Physics, Multidisciplinary
Barbara Prinari, A. David Trubatch, Bao-Feng Feng
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
Article
Mathematics, Applied
Aikaterini Gkogkou, Barbara Prinari, Bao-Feng Feng, A. David Trubatch
Summary: This paper develops the Riemann-Hilbert approach to the inverse scattering transform for the complex coupled short-pulse equation and obtains soliton solutions. The zoology of soliton solutions for the coupled system is richer than in the scalar case, including fundamental solitons, fundamental breathers, and composite breathers.
STUDIES IN APPLIED MATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Asela Abeya, Barbara Prinari, Gino Biondini, Panos G. Kevrekidis
Summary: The article investigates soliton solutions and interactions in a system of coupled nonlinear Schrodinger equations modeling the dynamics in one-dimensional repulsive Bose-Einstein condensates. Multi-soliton solutions are compactly represented using the Inverse Scattering Transform. The study includes a detailed characterization of canonical and non-canonical forms of solutions, as well as the classification of one-soliton solutions and their relationships to spectral data in the Inverse Scattering Transform.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Physics, Multidisciplinary
Asela Abeya, Gino Biondini, Barbara Prinari
Summary: We characterize the initial value problems for the defocusing Manakov system with nonzero background and spatial parity symmetry. The study reveals that the symmetries induced by parity are more complicated than in the scalar case, and the dark solitons and dark-bright solitons have specific symmetric properties.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Mathematics, Applied
Francesco Demontis, Cornelis van der Mee
Summary: In this paper, we establish a connection between the scattering theory of the focusing AKNS system with equally sized nonvanishing boundary conditions and that of the matrix Schrodinger equation. By utilizing a (shifted) Miura transformation, the focusing matrix nonlinear Schrodinger equation is converted into a new nonlocal integrable equation. We propose a method to solve the reflectionless matrix nonlinear Schrodinger equation by applying the matrix triplet method and deriving the multisoliton solutions of the nonlocal equation.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Article
Mathematics, Applied
Francesco Demontis, Cornelis van der Mee
Summary: This paper relates the scattering theory of the focusing AKNS system with vanishing boundary conditions to that of the matrix Schrodinger equation. The corresponding Miura transformation converts the focusing matrix nonlinear Schrodinger equation into a new nonlocal integrable equation. By applying the matrix triplet method, the multisoliton solutions of the nonlocal integrable equation are obtained, proposing a new method to solve the matrix nonlinear Schrodinger equation.
STUDIES IN APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Vincent Caudrelier, Aikaterini Gkogkou, Barbara Prinari
Summary: This paper investigates the propagation of ultrashort optical pulses in nonlinear birefringent fibers, using the dressing method and Darboux matrices for various types of solitons. The study reveals the explicit formulas for the polarization shift of fundamental solitons and interactions of other types of solitons.
STUDIES IN APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Francesco Demontis, Cornelis van der Mee
Summary: In this article, quaternionic linear algebra and quaternionic linear system theory are applied to develop the inverse scattering transform theory for the nonlinear Schrodinger equation with nonvanishing boundary conditions. The soliton solutions are also determined using triplets of quaternionic matrices.
RICERCHE DI MATEMATICA
(2023)
Review
Mathematics, Applied
Barbara Prinari
Summary: This topical review paper provides a survey of classical and more recent results on the inverse scattering transform (IST) for one-dimensional scalar, vector and square matrix NLS systems with physically relevant non-zero boundary conditions at space infinity. It discusses new developments and applications, and offers perspectives on future directions in this field.
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
(2023)
Article
Physics, Fluids & Plasmas
Gino Biondini, Antonio Moro, Barbara Prinari, Oleg Senkevich
Summary: In this study, the mean-field analog of the p-star model for homogeneous random networks is compared with the p-star model and its classical mean-field approximation in the thermodynamic regime. It is shown that the partition function of the mean-field model satisfies a sequence of partial differential equations known as the heat hierarchy, and the models connectance is obtained as a solution of a hierarchy of nonlinear viscous PDEs.
Article
Mathematics, Applied
F. Demontis, G. Ortenzi, M. Sommacal, C. van der Mee
RICERCHE DI MATEMATICA
(2019)
Article
Mathematics, Applied
F. Demontis, G. Ortenzi, M. Sommacal, C. van der Mee
RICERCHE DI MATEMATICA
(2019)
