Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation

Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions

(2019) Wen-Xiu Ma   East Asian Journal on Applied Mathematics

Lump-type solutions and interaction solutions for the (2+1)-dimensional generalized fifth-order KdV equation

(2018) Jian-Guo Liu   APPLIED MATHEMATICS LETTERS

Resonant multiple wave solutions to a new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation: Linear superposition principle

(2018) Fu-Hong Lin et al.   APPLIED MATHEMATICS LETTERS

General lump-type solutions of the (3+1)-dimensional Jimbo–Miwa equation

(2018) Xuelin Yong et al.   APPLIED MATHEMATICS LETTERS

Lump solutions to a (2+1)-dimensional extended KP equation

(2018) Solomon Manukure et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Diversity of exact solutions to a (3+1)-dimensional nonlinear evolution equation and its reduction

(2018) Yu-Hang Yin et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Diversity of interaction solutions to the (2+1)-dimensional Ito equation

(2018) Wen-Xiu Ma et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Lump solutions to a generalized Bogoyavlensky-Konopelchenko equation

(2018) Shou-Ting Chen et al.   Frontiers of Mathematics in China

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

(2018) Wen-Xiu Ma et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Interaction phenomenon to dimensionally reduced p-gBKP equation

(2018) Runfa Zhang et al.   MODERN PHYSICS LETTERS B

Mixed interactions of localized waves in the three-component coupled derivative nonlinear Schrödinger equations

(2018) Tao Xu et al.   NONLINEAR DYNAMICS

General high-order rogue waves to nonlinear Schrödinger–Boussinesq equation with the dynamical analysis

(2018) Xiaoen Zhang et al.   NONLINEAR DYNAMICS

M-lump and interactive solutions to a (3 $${+}$$+ 1)-dimensional nonlinear system

(2018) Yan Zhang et al.   NONLINEAR DYNAMICS

Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations

(2018) Bo Yang et al.   NONLINEAR DYNAMICS

Analytic study on interactions between periodic solitons with controllable parameters

(2018) Xiaoyan Liu et al.   NONLINEAR DYNAMICS

Interactions of vector anti-dark solitons for the coupled nonlinear Schrödinger equation in inhomogeneous fibers

(2018) Yujia Zhang et al.   NONLINEAR DYNAMICS

Lump solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation

(2018) Shou-Ting Chen et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A study of lump-type and interaction solutions to a (3+1)-dimensional Jimbo–Miwa-like equation

(2018) Sumayah Batwa et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Abundant lumps and their interaction solutions of (3+1)-dimensional linear PDEs

(2018) Wen-Xiu Ma   JOURNAL OF GEOMETRY AND PHYSICS

The study of lump solution and interaction phenomenon to (2+1)-dimensional potential Kadomstev–Petviashvili equation

(2018) Jianqing Lü et al.   Analysis and Mathematical Physics

Lump-type solutions and interaction solutions in the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

(2018) Min-Jie Dong et al.   Analysis and Mathematical Physics

Lump soliton, mixed lump stripe and periodic lump solutions of a (2 + 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

(2017) Zhonglong Zhao et al.   MODERN PHYSICS LETTERS B

New periodic solitary wave solutions for the new (2+1)-dimensional Korteweg–de Vries equation

(2017) Ye-Zhou Li et al.   NONLINEAR DYNAMICS

Bäcklund transformation, multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation

(2017) Li-Na Gao et al.   NONLINEAR DYNAMICS

Deformation rogue wave to the (2+1)-dimensional KdV equation

(2017) Xiaoen Zhang et al.   NONLINEAR DYNAMICS

Interaction solutions between lump and other solitons of two classes of nonlinear evolution equations

(2017) Yaning Tang et al.   NONLINEAR DYNAMICS

Lump solutions of a ( $$2+1$$ 2 + 1 )-dimensional bSK equation

(2017) Jianqing Lv et al.   NONLINEAR DYNAMICS

Rogue wave-type solutions of the mKdV equation and their relation to known NLSE rogue wave solutions

(2017) A. Ankiewicz et al.   NONLINEAR DYNAMICS

Lump dynamics of a generalized two-dimensional Boussinesq equation in shallow water

(2017) Xing Lü et al.   NONLINEAR DYNAMICS

Soliton-like, periodic wave and rational solutions for a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid

(2017) Shu-Liang Jia et al.   SUPERLATTICES AND MICROSTRUCTURES

A general sub-equation method to the burgers-like equation

(2017) Xiao-Min Wang et al.   Thermal Science

Rogue waves and lump solitons for a -dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

(2017) Yan Sun et al.   Waves in Random and Complex Media

Lump and lump-soliton solutions to the $$(2+1)$$ ( 2 + 1 ) -dimensional Ito equation

(2017) Jin-Yun Yang et al.   Analysis and Mathematical Physics

A note on rational solutions to a Hirota-Satsuma-like equation

(2016) Xing Lü et al.   APPLIED MATHEMATICS LETTERS

Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order

(2016) Xing Lü et al.   Communications in Nonlinear Science and Numerical Simulation

Solitary waves with the Madelung fluid description: A generalized derivative nonlinear Schrödinger equation

(2016) Xing Lü et al.   Communications in Nonlinear Science and Numerical Simulation

Rational solutions to an extended Kadomtsev-Petviashvili-like equation with symbolic computation

(2016) Xing Lü et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Resonant behavior of multiple wave solutions to a Hirota bilinear equation

(2016) Li-Na Gao et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

New three-wave solutions for the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

(2016) Jian-Guo Liu et al.   NONLINEAR DYNAMICS

Lump solutions to the ( $$\mathbf 2+1 $$ 2 + 1 )-dimensional Sawada–Kotera equation

(2016) Hai-Qiang Zhang et al.   NONLINEAR DYNAMICS

Two-mode fifth-order KdV equations: necessary conditions for multiple-soliton solutions to exist

(2016) Abdul-Majid Wazwaz   NONLINEAR DYNAMICS

Constructing lump solutions to a generalized Kadomtsev–Petviashvili–Boussinesq equation

(2016) Xing Lü et al.   NONLINEAR DYNAMICS

Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation

(2016) Xing Lü et al.   NONLINEAR DYNAMICS

A direct bilinear Bäcklund transformation of a (2+1)-dimensional Korteweg–de Vries-like model

(2015) Xing Lü et al.   APPLIED MATHEMATICS LETTERS

Constructing rogue wave prototypes of nonlinear evolution equations via an extended tanh method

(2015) Zhuosheng Lü et al.   CHAOS SOLITONS & FRACTALS

Nonlinear dynamic characterization of a new hysteretic device: experiments and computations

(2015) Biagio Carboni et al.   NONLINEAR DYNAMICS

Envelope bright- and dark-soliton solutions for the Gerdjikov–Ivanov model

(2015) Xing Lü et al.   NONLINEAR DYNAMICS

Lump solutions to dimensionally reduced $$\varvec{p}$$ p -gKP and $$\varvec{p}$$ p -gBKP equations

(2015) Wen Xiu Ma et al.   NONLINEAR DYNAMICS

Lump solutions to the Kadomtsev–Petviashvili equation

(2015) Wen-Xiu Ma   PHYSICS LETTERS A

Nonlinear parametric modeling of suspension bridges under aeroelastic forces: torsional divergence and flutter

(2012) Andrea Arena et al.   NONLINEAR DYNAMICS