New solutions for \((1+1)\)-dimensional and \((2+1)\)-dimensional Itô equations

DOI10.1155/2012/537930zbMath1264.35080OpenAlexW1524536358WikidataQ58912057 ScholiaQ58912057MaRDI QIDQ1954891

M. Sh. Alhuthali, Mohamed A. Abdelkawy, Ali H. Bhrawy

Publication date: 11 June 2013

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/537930

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solutions to PDEs in closed form (35C05) Software, source code, etc. for problems pertaining to partial differential equations (35-04) Soliton solutions (35C08)

Related Items (4)

Solutions of nonlinear integro-partial differential equations by the method of \((G^\prime/G, 1/G)\) ⋮ Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Itô system ⋮ High-dimensional nonlinear wave transitions and their mechanisms ⋮ On the integrability of the (1+1)‐dimensional and (2+1)‐dimensional Ito equations

Cites Work

• New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method
• Solving nonlinear partial differential equations by the sn-ns method
• Multi-symplectic methods for the Itô-type coupled KdV equation
• Exact travelling wave solutions of the Schamel-Korteweg-de Vries equation
• Exact 1-soliton solution of the Zakharov equation in plasmas withpower law nonlinearity
• The \(\frac{G'}{G}\) method and 1-soliton solution of the Davey-Stewartson equation
• Analytic study on the higher order Itô equations: new solitary wave solutions using the Exp-function method
• An improved generalized \(F\)-expansion method and its application to the \((2 + 1)\)-dimensional KdV equations
• Bifurcations of travelling wave solutions in the \((N + 1)\)-dimensional sine-cosine-Gordon equations
• Solutions of coupled KdV-type equations
• The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation
• Extended \(F\)-expansion method and periodic wave solutions for the generalized Zakharov equations
• Multiple-soliton solutions for the generalized \((1+1)\)-dimensional and the generalized \((2+1)\)-dimensional Itô equations
• New traveling waves solutions to generalized Kaup-Kupershmidt and Ito equations
• 1-soliton solution of the generalized Zakharov equation in plasmas by He's variational principle
• Exact solutions for a third-order KdV equation with variable coefficients and forcing term
• Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation
• Exact solutions for the generalized BBM equation with variable coefficients
• Travelling wave solutions for time-delayed nonlinear evolution equations
• 1-soliton solution of the coupled KdV equation and Gear-Grimshaw model
• Inverse scattering method and vector higher order nonlinear Schrödinger equation
• Generalized extended tanh-function method and its application to \((1+1)\)-dimensional dispersive long wave equation
• New solutions for (1+1)-dimensional and (2+1)-dimensional Kaup--Kupershmidt equations
• Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method
• Periodical solution to the nonlinear dissipative equation for surface waves in a convecting liquid layer
• The double F-expansion approach and novel nonlinear wave solutions of soliton equation in (2 + 1)-dimension
• The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants
• Extended tanh-function method and its applications to nonlinear equations
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• A general approach to hyperbolic partial differential equations by homotopy perturbation method
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Nonlinear superposition formulae of the Ito equation and a model equation for shallow water waves
• Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method
• Exact periodic solutions of the complex Ginzburg–Landau equation
• N -Soliton-like Solution of Ito Equation
• Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
• Some general periodic solutions to coupled nonlinear Schrödinger equations.

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