Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation

Ronald Adams; S. C. Mancas; Stefani Mancas

doi:10.1016/j.amc.2017.11.005

Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation

Ronald Adams, S. C. Mancas, Stefani Mancas

Embry-Riddle Aeronautical University

Research output: Contribution to journal › Article › peer-review

Abstract

 We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions
 (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term.
 The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal
 waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity
 properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally)
 stable.

Original language	American English
Journal	Applied Mathematics and Computation
Volume	321
DOIs	https://doi.org/10.1016/j.amc.2017.11.005
State	Published - Mar 15 2018

Keywords

cnodial waves
solitary waves
fifth order KdV equation
stability of traveling waves

Disciplines

Physical Sciences and Mathematics

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10.1016/j.amc.2017.11.005License: Unspecified

Cite this

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title = "Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation",

abstract = " We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.",

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author = "Ronald Adams and Mancas, {S. C.} and Stefani Mancas",

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day = "15",

doi = "10.1016/j.amc.2017.11.005",

language = "American English",

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T1 - Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation

AU - Adams, Ronald

AU - Mancas, S. C.

AU - Mancas, Stefani

PY - 2018/3/15

Y1 - 2018/3/15

N2 - We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.

AB - We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.

KW - cnodial waves

KW - solitary waves

KW - fifth order KdV equation

KW - stability of traveling waves

UR - http://www.sciencedirect.com/science/article/pii/S0096300317307786

U2 - 10.1016/j.amc.2017.11.005

DO - 10.1016/j.amc.2017.11.005

M3 - Article

SN - 1873-5649

VL - 321

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation

Abstract

Keywords

Disciplines

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