Exact solutions for stochastic mKdV equations

DOI10.1016/S0960-0779(03)00089-4zbMath1068.35147MaRDI QIDQ1432933

Yingchao Xie

Publication date: 1 July 2004

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (22)

Positonic solutions for Wick-type stochastic KdV equations ⋮ Exact solutions of the Wick-type stochastic Kadomtsev-Petviashvili equations ⋮ Stochastic exact solutions of the Wick-type stochastic NLS equation ⋮ Three types of exact solutions to Wick-type generalized stochastic Korteweg-de Vries equation ⋮ New exact solutions for the Wick-type stochastic Zakharov-Kuznetsov equation for modelling waves on shallow water surfaces ⋮ Periodic-like solutions of variable coefficient and Wick-type stochastic NLS equations ⋮ White noise solutions to the stochastic mKdV equation ⋮ Application of rational expansion method for stochastic differential equations ⋮ White noise functional solutions of Wick-type stochastic generalized Hirota-Satsuma coupled KdV equations ⋮ Analytical solutions for the stochastic Gardner equation ⋮ Exact solutions of \((2+1)\)-dimensional stochastic Broer-Kaup equation ⋮ Exact solutions to generalized Wick-type stochastic Kadomtsev-Petviashvili equation ⋮ A modified Jacobi elliptic function expansion method and its application to Wick-type stochastic KdV equation ⋮ New solutions for the Wick-type 2-dimensional stochastic compound KdV equations ⋮ Exact solutions for Wick-type stochastic coupled KdV equations ⋮ Exact solutions for the Wick-type stochastic 2-dimensional KdV equations with dissipation ⋮ Exact solutions of the Wick-type stochastic mKP equation ⋮ New exact Jacobian elliptic function solutions for Wick-type stochastic KdV equation ⋮ Symmetry reductions and soliton-like solutions for stochastic MKdV equation ⋮ An auto-Bäcklund transformation and exact solutions of stochastic Wick-type Sawada-Kotera equations ⋮ Exact solutions for generalized stochastic Wick-type KdV-mKdV equations ⋮ A series of exact solutions for (2 + 1)-dimensional Wick-type stochastic generalized Broer-Kaup system via a modified variable-coefficient projective Riccati equation mapping method

Cites Work

• On the stochastic Korteweg-de Vries equation
• The stochastic Korteweg-de Vries equation in \(L^2(\mathbb{R})\)
• A remark on the equivalence between Poisson and Gaussian stochastic partial differential equations
• Numerical simulation of the stochastic Korteweg-de Vries equation
• Exact solutions for a compound KdV-Burgers equation
• White noise driven Korteweg-de Vries equation
• A new Bäcklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients
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