Symbolic computation on a (2+1)-dimensional generalized variable-coefficient Boiti–Leon–Pempinelli system for the water waves

Generalized Darboux transformation and the higher-order semirational solutions for a non-linear Schrödinger system in a birefringent fiber

(2021) Dan-Yu Yang et al.   MODERN PHYSICS LETTERS B

Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

(2021) Yuan Shen et al.   PHYSICA SCRIPTA

Optical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient nonlinear Schrödinger system

(2021) Xin-Yi Gao et al.   APPLIED MATHEMATICS LETTERS

Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics

(2021) Fei-Yan Liu et al.   CHAOS SOLITONS & FRACTALS

Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models

(2021) Aly R. Seadawy et al.   CHAOS SOLITONS & FRACTALS

Breather-wave, periodic-wave and traveling-wave solutions for a (2 + 1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation for an incompressible fluid

(2021) Yuan Shen et al.   MODERN PHYSICS LETTERS B

Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

(2021) Dong Wang et al.   NONLINEAR DYNAMICS

Fusion and fission phenomena of X-type, Y-type and periodic lump-stripe soliton solutions for a (3 + 1)-dimensional generalized nonlinear evolution equation arising in shallow water waves

(2021) Yuan Shen et al.   PHYSICS LETTERS A

Higher-order hybrid waves for the (2 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid via the modified Pfaffian technique

(2021) Lei Hu et al.   ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

Soliton, multiple-lump and hybrid solutions of a (2+1)-dimensional generalized Hirota-Satsuma-Ito equation for the water waves

(2021) Meng Wang et al.   European Physical Journal Plus

Lie group analysis and analytic solutions for a (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation in fluid mechanics and plasma physics

(2021) Fei-Yan Liu et al.   European Physical Journal Plus

Vector bright solitons and their interactions of the couple Fokas–Lenells system in a birefringent optical fiber

(2020) Chen-Rong Zhang et al.   ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

Bilinear form, solitons, breathers and lumps of a (3 + 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation in ocean dynamics, fluid mechanics and plasma physics

(2020) Yu-Jie Feng et al.   European Physical Journal Plus

Lax pair, conservation laws, Darboux transformation, breathers and rogue waves for the coupled nonautonomous nonlinear Schrödinger system in an inhomogeneous plasma

(2020) Cui-Cui Ding et al.   CHAOS SOLITONS & FRACTALS

Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma

(2020) Xia-Xia Du et al.   CHAOS SOLITONS & FRACTALS

Lump, mixed lump-stripe, mixed rogue wave-stripe and breather wave solutions for a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation

(2020) Shao-Hua Liu et al.   MODERN PHYSICS LETTERS B

Bilinear form, soliton, breather, lump and hybrid solutions for a ($$\varvec{2+1}$$)-dimensional Sawada–Kotera equation

(2020) Liu-Qing Li et al.   NONLINEAR DYNAMICS

Viewing the Solar System via a variable-coefficient nonlinear dispersive-wave system

(2020) Xin-Yi Gao et al.   ACTA MECHANICA

Magneto-optical/ferromagnetic-material computation: Bäcklund transformations, bilinear forms and N solitons for a generalized (3+1)-dimensional variable-coefficient modified Kadomtsev–Petviashvili system

(2020) Xin-Yi Gao et al.   APPLIED MATHEMATICS LETTERS

Bilinear forms through the binary Bell polynomials, N solitons and Bäcklund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach

(2020) Xin-Yi Gao et al.   COMMUNICATIONS IN THEORETICAL PHYSICS

Breather, lump, shock and travelling-wave solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid mechanics and plasma physics

(2020) Shao-Hua Liu et al.   INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Dark–dark solitons for the coupled spatially modulated Gross–Pitaevskii system in the Bose–Einstein condensation

(2020) Xin Zhao et al.   MODERN PHYSICS LETTERS B

Reduction and analytic solutions of a variable-coefficient Korteweg–de Vries equation in a fluid, crystal or plasma

(2020) Yu-Qi Chen et al.   MODERN PHYSICS LETTERS B

Hetero-Bäcklund transformation and similarity reduction of an extended (2+1)-dimensional coupled Burgers system for fluid mechanics

(2020) Xin-Yi Gao et al.   PHYSICS LETTERS A

Comment on “Bilinear form, solitons, breathers and lumps of a $$(3+1)$$-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation in ocean dynamics, fluid mechanics and plasma physics” [Eur. Phys. J. Plus (2020) 135:272]

(2020) Xin-Yi Gao et al.   European Physical Journal Plus

Lax pairs, Darboux transformation, bilinear forms and solitonic interactions for a combined Calogero-Bogoyavlenskii-Schiff-type equation

(2020) Ting-Ting Jia et al.   APPLIED MATHEMATICS LETTERS

Shallow water in an open sea or a wide channel: Auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system

(2020) Xin-Yi Gao et al.   CHAOS SOLITONS & FRACTALS

Solitons and periodic waves for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics

(2020) Dong Wang et al.   COMMUNICATIONS IN THEORETICAL PHYSICS

Ablowitz–Kaup–Newell–Segur system, conservation laws and Bäcklund transformation of a variable-coefficient Korteweg–de Vries equation in plasma physics, fluid dynamics or atmospheric science

(2020) Yu-Qi Chen et al.   INTERNATIONAL JOURNAL OF MODERN PHYSICS B

Bilinear forms and soliton solutions for a (2 + 1)-dimensional variable-coefficient nonlinear Schrödinger equation in an optical fiber

(2020) Dong Wang et al.   MODERN PHYSICS LETTERS B

Darboux-dressing transformation, semi-rational solutions, breathers and modulation instability for the cubic-quintic nonlinear Schrödinger system with variable coefficients in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

(2020) Dan-Yu Yang et al.   PHYSICA SCRIPTA

Long waves in oceanic shallow water: Symbolic computation on the bilinear forms and Bäcklund transformations for the Whitham–Broer–Kaup system

(2020) Xin-Yi Gao et al.   European Physical Journal Plus

Generalized Darboux transformation, solitonic interactions and bound states for a coupled fourth-order nonlinear Schrödinger system in a birefringent optical fiber

(2020) Meng Wang et al.   APPLIED MATHEMATICS LETTERS

Oceanic studies via a variable-coefficient nonlinear dispersive-wave system in the Solar System

(2020) Xin-Yi Gao et al.   CHAOS SOLITONS & FRACTALS

In oceanography, acoustics and hydrodynamics: an extended coupled (2+1)-dimensional Burgers system

(2020) Xin-Yi Gao et al.   CHINESE JOURNAL OF PHYSICS

Superregular solutions for a coupled nonlinear Schrödinger system in a two-mode nonlinear fiber

(2020) He-yuan Tian et al.   PHYSICA SCRIPTA

Time fractional diffusion equation for shipping water events simulation

(2020) M.A. González-Olvera et al.   CHAOS SOLITONS & FRACTALS

Dark breather waves, dark lump waves and lump wave–soliton interactions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in a fluid

(2019) Cong-Cong Hu et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Generalized Darboux Transformations, Rogue Waves, and Modulation Instability for the Coherently Coupled Nonlinear Schrödinger Equations in Nonlinear Optics

(2019) Su-Su Chen et al.   ANNALEN DER PHYSIK

Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev-Petviashvili equation in fluid mechanics

(2019) Meng Wang et al.   CHINESE JOURNAL OF PHYSICS

Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+1)-dimensional nonlinear wave equation for a liquid with gas bubbles

(2019) Meng Wang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Breather and hybrid solutions for a generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation for the water waves

(2019) Cui-Cui Ding et al.   NONLINEAR DYNAMICS

Symmetry Reductions, Group‐Invariant Solutions, and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

(2019) Xia‐Xia Du et al.   ANNALEN DER PHYSIK

Quintic time-dependent-coefficient derivative nonlinear Schrödinger equation in hydrodynamics or fiber optics: bilinear forms and dark/anti-dark/gray solitons

(2019) Ting-Ting Jia et al.   NONLINEAR DYNAMICS

Soliton interactions of a variable-coefficient three-component AB system for the geophysical flows

(2019) Yu-Jie Feng et al.   MODERN PHYSICS LETTERS B

Solitons for the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid via the Pfaffian technique

(2019) Lei Hu et al.   MODERN PHYSICS LETTERS B

Solitons and periodic waves for the (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

(2019) Gao-Fu Deng et al.   NONLINEAR DYNAMICS

Lump, lumpoff and rogue waves for a (2 + 1)-dimensional reduced Yu-Toda-Sasa-Fukuyama equation in a lattice or liquid

(2019) Meng Wang et al.   European Physical Journal Plus

Investigation of breaking dynamics for Riemann waves in shallow water

(2019) R. Saleh et al.   CHAOS SOLITONS & FRACTALS

Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Bäcklund transformations

(2019) Xin-Yi Gao et al.   APPLIED MATHEMATICS LETTERS

Similarity Reduction and Exact Solutions of a Boussinesq-like Equation

(2018) Bo Zhang et al.   ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES

Lax pair, binary Darboux transformations and dark-soliton interaction of a fifth-order defocusing nonlinear Schrödinger equation for the attosecond pulses in the optical fiber communication

(2018) Su-Su Chen et al.   Waves in Random and Complex Media

Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows

(2018) Jing-Jing Su et al.   APPLIED MATHEMATICS LETTERS

Bäcklund transformations for the Jacobi system on an ellipsoid

(2017) A. V. Tsiganov   THEORETICAL AND MATHEMATICAL PHYSICS

Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

(2015) Hong-Li An et al.   COMMUNICATIONS IN THEORETICAL PHYSICS

Comment on “Solitons, Bäcklund transformation, and Lax pair for the (2 + 1)-dimensional Boiti-Leon- Pempinelli equation for the water waves” [J. Math. Phys. 51, 093519 (2010)]

(2015) Xin-Yi Gao   JOURNAL OF MATHEMATICAL PHYSICS

Soliton Equations and Simple Combinatorics

(2008) Franklin Lambert et al.   ACTA APPLICANDAE MATHEMATICAE