scholarly journals Frequency-Uniform Decomposition, Function Spaces , and Applications to Nonlinear Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Shaolei Ru ◽  
Jiecheng Chen
Keyword(s):  
Cauchy Problem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Function Spaces ◽  
Nonlinear Evolution Equations ◽  
Ginzburg Landau ◽  
New Class ◽  
The Cauchy Problem ◽  
Ginzburg Landau Equations

By combining frequency-uniform decomposition with (), we introduce a new class of function spaces (denoted by ). Moreover, we study the Cauchy problem for the generalized NLS equations and Ginzburg-Landau equations in .

scholarly journals Generalized quasilinear hyperbolic equations and Yosida approximations

2003 ◽  
Vol 74 (1) ◽  
pp. 69-86 ◽  
Author(s):  
Jong Yeoul Park ◽  
Il Hyo Jung ◽  
Yong Han Kang
Keyword(s):  
Cauchy Problem ◽  
Boundary Conditions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Hyperbolic Equations ◽  
Global Solutions ◽  
Global Solvability ◽  
Nonlinear Evolution Equations ◽  
Damping Term ◽  
The Cauchy Problem

AbstractWe will show the existence, uniqueness and regularity of global solutions for the Cauchy problem for nonlinear evolution equations with the damping term .As an application of our results, we give the global solvability and regularity of the mixed problem with Dirichiet boundary conditions:

Auto-Bäcklund Transformation and Solitary-wave Solutions to Non- integrable Generalized Fifth-order Nonlinear Evolution Equations

1999 ◽  
Vol 54 (8-9) ◽  
pp. 549-553 ◽  
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Solitary Wave ◽  
Symbolic Computation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
New Class ◽  
Wave Solutions ◽  
Fifth Order ◽  
Truncated Painlevé Expansion

We show that the application of the truncated Painlevé expansion and symbolic computation leads to a new class of analytical solitary-wave solutions to the general fifth-order nonlinear evolution equations which include Lax, Sawada-Kotera (SK), Kaup-Kupershmidt (KK), and Ito equations. Some explicit solitary-wave solutions are presented.

Sign in / Sign up

Export Citation Format

Share Document