Bäcklund transformation of potentials of the Korteweg-devries equation and the interaction of solitons with cnoidal waves

Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications - Lecture Notes in Mathematics ◽

10.1007/bfb0081167 ◽

1976 ◽

pp. 162-183 ◽

Cited By ~ 13

Author(s):

Hugo D. Wahlquist

Keyword(s):

Bäcklund Transformation ◽

Backlund Transformation ◽

Cnoidal Waves ◽

Interaction Of Solitons

Download Full-text

A Truncated Painlevé Expansion and Exact Analytical Solutions for the Nonlinear Schr¨Odinger Equation with Variable Coefficients

Zeitschrift für Naturforschung A ◽

10.1515/zna-2005-11-1202 ◽

2005 ◽

Vol 60 (11-12) ◽

pp. 768-774 ◽

Cited By ~ 3

Author(s):

Biao Li ◽

Yong Chen

Keyword(s):

Analytical Solutions ◽

Bäcklund Transformation ◽

Variable Coefficients ◽

Backlund Transformation ◽

Exact Analytical Solutions ◽

Interaction Of Solitons ◽

Varying Dispersion ◽

Physical Phenomena ◽

Truncated Painlevé Expansion ◽

Singular Soliton

By using the truncated Painlevé expansion analysis an auto-Bäcklund transformation is found for the nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption. Then, based on the obtained auto-Bäcklund transformation and symbolic computation, we explore some explicit exact solutions including soliton-like solutions, singular soliton-like solutions, which may be useful to explain the corresponding physical phenomena. Further, the formation and interaction of solitons are simulated by computer. - PACS Nos.: 05.45.Yv, 02.30.Jr, 42.65.Tg

Download Full-text

Bilinear Bäcklund transformation, N ‐soliton, and infinite conservation laws for Lax–Kadomtsev–Petviashvili and generalized Korteweg–de Vries equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7516 ◽

2021 ◽

Author(s):

Shrouk Wael ◽

Aly R. Seadawy ◽

Salah M. Moawad ◽

Omar H. El‐Kalaawy

Keyword(s):

Conservation Laws ◽

Bäcklund Transformation ◽

Backlund Transformation ◽

Bilinear Bäcklund Transformation ◽

De Vries

Download Full-text

Casoratian Solutions to Toda Lattice Via Its Bäcklund Transformation

Communications in Theoretical Physics ◽

10.1088/0253-6102/53/3/06 ◽

2010 ◽

Vol 53 (3) ◽

pp. 435-439

Author(s):

Xuan Qi-Fei ◽

Zhang Da-Jun ◽

Zhou Jing

Keyword(s):

Toda Lattice ◽

Bäcklund Transformation ◽

Backlund Transformation

Download Full-text

A One-Parameter Bäcklund Transformation for the Euclidean Liouville and Wave Equations

Physica Scripta ◽

10.1088/0031-8949/27/5/001 ◽

1983 ◽

Vol 27 (5) ◽

pp. 321-322 ◽

Cited By ~ 1

Author(s):

Huang Xun-Cheng

Keyword(s):

Wave Equations ◽

Bäcklund Transformation ◽

Backlund Transformation

Download Full-text

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

Waves in Random and Complex Media ◽

10.1080/17455030.2016.1185193 ◽

2016 ◽

Vol 27 (1) ◽

pp. 1-14 ◽

Cited By ~ 10

Author(s):

Zi-Jian Xiao ◽

Bo Tian ◽

Hui-Ling Zhen ◽

Jun Chai ◽

Xiao-Yu Wu

Keyword(s):

Bäcklund Transformation ◽

Kdv Equation ◽

Soliton Solutions ◽

Backlund Transformation

Download Full-text

Solitonic solutions and Bäcklund transformation for the inhomogeneous N-coupled nonlinear Schrödinger equations

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2008.09.033 ◽

2009 ◽

Vol 388 (2-3) ◽

pp. 209-217 ◽

Cited By ~ 13

Author(s):

Xiang-Hua Meng ◽

Bo Tian ◽

Tao Xu ◽

Hai-Qiang Zhang ◽

Qian Feng

Keyword(s):

Bäcklund Transformation ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Backlund Transformation ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

Download Full-text

Generating the Bogomolny-Prasad-Sommerfield One-Monopole Solution by a Bäcklund Transformation

Physical Review Letters ◽

10.1103/physrevlett.45.505 ◽

1980 ◽

Vol 45 (7) ◽

pp. 505-508 ◽

Cited By ~ 44

Author(s):

Peter Forgács ◽

Zalán Horváth ◽

László Palla

Keyword(s):

Bäcklund Transformation ◽

Backlund Transformation ◽

Monopole Solution

Download Full-text

Bäcklund transformation, residual symmetry and exact interaction solutions of an extended (2+1)-dimensional Korteweg–de Vries equation

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107640 ◽

2021 ◽

pp. 107640

Author(s):

Huiling Wu ◽

Qiaoyun Chen ◽

Junfeng Song

Keyword(s):

Vries Equation ◽

Bäcklund Transformation ◽

Backlund Transformation ◽

Residual Symmetry ◽

Interaction Solutions ◽

De Vries

Download Full-text

N-dimensional Auto-Bäcklund transformation and exact solutions to n-dimensional Burgers system

Applied Mathematics Letters ◽

10.1016/j.aml.2016.07.019 ◽

2017 ◽

Vol 63 ◽

pp. 46-52 ◽

Cited By ~ 9

Author(s):

Mingliang Wang ◽

Jinliang Zhang ◽

Xiangzheng Li

Keyword(s):

Exact Solutions ◽

Bäcklund Transformation ◽

Backlund Transformation ◽

Burgers System

Download Full-text

Analytical study on a two-dimensional Korteweg–de Vries model with bilinear representation, Bäcklund transformation and soliton solutions

Applied Mathematical Modelling ◽

10.1016/j.apm.2014.10.046 ◽

2015 ◽

Vol 39 (12) ◽

pp. 3221-3226 ◽

Cited By ~ 84

Author(s):

Xing Lü ◽

Fuhong Lin ◽

Fenghua Qi

Keyword(s):

Analytical Study ◽

Bäcklund Transformation ◽

Soliton Solutions ◽

Two Dimensional ◽

Backlund Transformation ◽

De Vries

Download Full-text