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Comment on: ”Multi soliton solution, rational solution of the BoussinesqBurgers equations”
"... We demonstrate that all ”new ” exact solutions of the Boussinesq ..."
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Cited by 1 (1 self)
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We demonstrate that all ”new ” exact solutions of the Boussinesq
Multisolitons
, 2001
"... We derive the KadomtsevPetviashvili (KP) equation defined over a general associative algebra and construct its Nsoliton solution. For the example of the Moyal algebra, we find multisoliton solutions for arbitrary spacespace noncommutativity. The noncommutativity of coordinates is shown to obstru ..."
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We derive the KadomtsevPetviashvili (KP) equation defined over a general associative algebra and construct its Nsoliton solution. For the example of the Moyal algebra, we find multisoliton solutions for arbitrary spacespace noncommutativity. The noncommutativity of coordinates is shown
RESEARCH ARTICLE A Generalized Simplest Equation Method and Its Application to the BoussinesqBurgers Equation
"... In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a B ..."
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Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, nontraveling wave solutions, multisoliton solutions, rational solutions
Soliton solutions of the KP equation and application to shallow water waves
"... Abstract. The main purpose of this paper is to give a survey of recent developments on a classification of soliton solutions of the KP equation. The paper is selfcontained, and we give complete proofs of theorems needed for the classification. The classification is based on the totally nonnegative ..."
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Cited by 24 (9 self)
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detailed description of the soliton solutions associated with Gr(2, 4), which play a fundamental role in the study of multisoliton solutions. We then consider a physical application of some of those solutions related to the Mach reflection discussed by J. Miles in 1977. Contents
The calculation of multisoliton solutions of the Vakhnenko equation by the inverse scattering method
, 2001
"... A B€acklund transformation both in bilinear form and in ordinary form for the transformed Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse scattering method has a thirdorder eigenvalue problem. A procedure for finding the exact Nsoliton solution of the Vakhne ..."
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A B€acklund transformation both in bilinear form and in ordinary form for the transformed Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse scattering method has a thirdorder eigenvalue problem. A procedure for finding the exact Nsoliton solution
On a Shallow Water Wave Equation
 Program in Applied Mathematics (University of Colorado at
, 1993
"... In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et al [Stud. Appl. Math., ..."
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Cited by 2 (0 self)
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In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et al [Stud. Appl. Math.,
Vol.18(2014) No.3,pp.217223 On MultiSoliton Solution of DegasperisProcesi Equation with SelfConsistent Sources
, 2013
"... Abstract: DegasperisProcesi equation with selfconsistent sources is an integrable extension of the original system. We obtain the multisoliton solutions of the DegasperisProcesi equation with selfconsistent sources by using the reciprocal transformation and the Darboux transformation. ..."
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Abstract: DegasperisProcesi equation with selfconsistent sources is an integrable extension of the original system. We obtain the multisoliton solutions of the DegasperisProcesi equation with selfconsistent sources by using the reciprocal transformation and the Darboux transformation.
Dynamics of rogue waves on a multisoliton background in a vector nonlinear Schrödinger equation
, 2014
"... Abstract. General higher order rogue waves of a vector nonlinear Schrödinger equation (Manakov system) are derived using a Darbouxdressing transformation with an asymptotic expansion method. The Nth order semirational solutions containing 3N free parameters are expressed in separation of variabl ..."
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Abstract. General higher order rogue waves of a vector nonlinear Schrödinger equation (Manakov system) are derived using a Darbouxdressing transformation with an asymptotic expansion method. The Nth order semirational solutions containing 3N free parameters are expressed in separation
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