Exact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota’s approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

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Four-soliton solution and soliton interactions of the generalized coupled nonlinear Schrödinger equation

Chinese Physics B ◽

10.1088/1674-1056/ab84ce ◽

2020 ◽

Vol 29 (6) ◽

pp. 064211

Author(s):

Li-Jun Song ◽

Xiao-Ya Xu ◽

Yan Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Soliton Solution ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Soliton Interactions ◽

Nonlinear Schrödinger ◽

Coupled Nonlinear Schrödinger Equation

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Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential

Physical Review E ◽

10.1103/physreve.91.033202 ◽

2015 ◽

Vol 91 (3) ◽

Cited By ~ 136

Author(s):

Min Li ◽

Tao Xu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

The Self ◽

Soliton Interactions ◽

Symmetric Potential ◽

Nonlinear Schrödinger ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Nonlocal Nonlinear

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Soliton interactions and degenerate soliton complexes for the focusing nonlinear Schrödinger equation with nonzero background

The European Physical Journal Plus ◽

10.1140/epjp/i2018-12263-y ◽

2018 ◽

Vol 133 (10) ◽

Cited By ~ 5

Author(s):

Sitai Li ◽

Gino Biondini

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Soliton Interactions ◽

Nonlinear Schrödinger

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Dark-bright soliton interactions in coupled nonautonomous nonlinear Schrödinger equation with complex potentials

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2020.110560 ◽

2021 ◽

Vol 143 ◽

pp. 110560

Author(s):

Sudipta Nandy ◽

Abhijit Barthakur

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Complex Potentials ◽

Bright Soliton ◽

Soliton Interactions ◽

Nonlinear Schrödinger

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Addendum to ‘‘Simple multisoliton solutions’’: Multisolitons of the nonlinear Schrödinger equation

American Journal of Physics ◽

10.1119/1.13976 ◽

1985 ◽

Vol 53 (1) ◽

pp. 85-86

Author(s):

A‐M. M. Abdel‐Rahman

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Multisoliton Solutions

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COMPACTNESS OF THE SET OF MULTISOLITON SOLUTIONS OF THE NONLINEAR SCHRÖDINGER EQUATION

Sbornik Mathematics ◽

10.1070/sm1993v075n02abeh003392 ◽

1993 ◽

Vol 75 (2) ◽

pp. 429-443 ◽

Cited By ~ 1

Author(s):

D Sh Lundina ◽

V A Marchenko

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Multisoliton Solutions

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The Uncertainty Relation of One-Soliton Solution with Nonlinear Schrödinger Equation and Its Performance as an Analyzing Wavelet

Journal of the Physical Society of Japan ◽

10.1143/jpsj.67.361 ◽

1998 ◽

Vol 67 (2) ◽

pp. 361-364

Author(s):

Ryoya Saji ◽

Hidetoshi Konno

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Soliton Solution ◽

Schrodinger Equation ◽

Uncertainty Relation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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The soliton solution of a modified nonlinear schrödinger equation

Global Journal of Mathematical Analysis ◽

10.14419/gjma.v5i1.7074 ◽

2017 ◽

Vol 5 (1) ◽

pp. 16

Author(s):

Jumei Zhang ◽

Li Yin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Equations ◽

Nonlinear Schrödinger Equation ◽

Soliton Solution ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Derivative Method ◽

Hirota Bilinear

Hirota bilinear derivative method can be used to construct the soliton solutions for nonlinear equations. In this paper we construct the soliton solutions of a modified nonlinear Schrödinger equation by bilinear derivative method.

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DETERMINANT REPRESENTATION OF N-TIMES DARBOUX TRANSFORMATION FOR THE DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION

Modern Physics Letters B ◽

10.1142/s0217984913502163 ◽

2013 ◽

Vol 27 (29) ◽

pp. 1350216 ◽

Cited By ~ 2

Author(s):

JINGWEI HAN ◽

JING YU ◽

JINGSONG HE

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Soliton Solution ◽

Darboux Transformation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nls Equation ◽

Nonlinear Schrödinger ◽

Determinant Representation

The determinant expression T[N] of a new Darboux transformation (DT) for the Ablowitz–Kaup–Newell–Segur equation are given in this paper. By making use of this DT under the reduction r = q*, we construct determinant expressions of dark N-soliton solution for the defocusing NLS equation. Except known one-soliton, we provide smooth two-soliton and smooth N-soliton on a certain domain of parameter for the defocusing NLS equation.

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