scholarly journals Integrability of a nonlinear evolution equation derived from isoperimetric plane curve motion

2009 ◽  
Vol 50 (1) ◽  
pp. 013504
Author(s):  
J. C. Brunelli
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Plane Curve

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.

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