scholarly journals <i>N</i>-Fold Darboux Transformation for a Nonlinear Evolution Equation

2012 ◽  
Vol 03 (08) ◽  
pp. 943-948 ◽  
Author(s):  
Yannan Zhao
Keyword(s):  
Evolution Equation ◽  
Darboux Transformation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution

DARBOUX TRANSFORMATION AND VARIOUS SOLUTIONS FOR A NONLINEAR EVOLUTION EQUATION IN (3 + 1)-DIMENSIONS

2008 ◽  
Vol 22 (30) ◽  
pp. 2945-2966 ◽  
Author(s):  
ZHAQILAO ◽  
ZHI-BIN LI
Keyword(s):  
Evolution Equation ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Spectral Problems ◽  
Complexiton Solution

A new (3 + 1)-dimensional nonlinear evolution equation can be decomposed into three (1 + 1)-dimensional nonlinear evolution equations. In this paper, N-soliton solution, resonant solution and complexiton solution of the (3 + 1)-dimensional nonlinear evolution equation are obtained via an N-fold Darboux transformation of the Ablowitz–Kaup–Newell–Segur spectral problems.

scholarly journals Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

A NONLINEAR EVOLUTION EQUATION IN AN ORDERED SPACE, ARISING FROM KINETIC THEORY

2007 ◽  
Vol 09 (02) ◽  
pp. 217-251
Author(s):  
CECIL P. GRÜNFELD
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Sufficient Conditions ◽  
Existence Theory ◽  
The Cauchy Problem ◽  
Ordered Space ◽  
Coagulation Equation ◽  
Boltzmann Model ◽  
Classical Boltzmann Equation

We investigate the Cauchy problem for a nonlinear evolution equation, formulated in an abstract Lebesgue space, as a generalization of various Boltzmann kinetic models. Our main result provides sufficient conditions for the existence, uniqueness, and positivity of global in time solutions. The analysis extends nontrivially monotonicity methods, originally developed in the context of the existence theory for the classical Boltzmann equation in L1. Our application examples are Smoluchowski's coagulation equation, a Povzner-like equation with dissipative collisions, and a Boltzmann model with chemical reactions, for which we obtain a unitary existence theory, with improved results, compared to the literature.

Sign in / Sign up

Export Citation Format

Share Document