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Qualitative analysis and approximate damped oscillatory solutions for a kind of nonlinear dispersive-dissipative equation

Qualitative analysis and approximate damped oscillatory solutions for a kind of nonlinear... This paper makes qualitative analysis to the bounded traveling wave solutions for a kind of nonlinear dispersive-dissipative equation, and considers its solving problem. The relation is investigated between behavior of its solution and the dissipation coefficient. Further, all approximate damped oscillatory solutions when dissipation coefficient is small are presented by utilizing the method of undetermined coefficients according to the theory of rotated vector field in planar dynamical systems. Finally, error estimate is given by establishing the integral equation which reflects the relation between approximate and exact damped oscillatory solutions applying the idea of homogenization principle. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Qualitative analysis and approximate damped oscillatory solutions for a kind of nonlinear dispersive-dissipative equation

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-017-0632-y
Publisher site
See Article on Publisher Site

Abstract

This paper makes qualitative analysis to the bounded traveling wave solutions for a kind of nonlinear dispersive-dissipative equation, and considers its solving problem. The relation is investigated between behavior of its solution and the dissipation coefficient. Further, all approximate damped oscillatory solutions when dissipation coefficient is small are presented by utilizing the method of undetermined coefficients according to the theory of rotated vector field in planar dynamical systems. Finally, error estimate is given by establishing the integral equation which reflects the relation between approximate and exact damped oscillatory solutions applying the idea of homogenization principle.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 15, 2017

References