Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

DOI10.1080/17455030.2011.606853zbMath1274.76167OpenAlexW2084457368MaRDI QIDQ2855378

Anjan Biswas, E. V. Krishnan, Ghodrat Ebadi, Essaid Zerrad, Manel Labidi

Publication date: 25 October 2013

Published in: Waves in Random and Complex Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17455030.2011.606853

zbMATH Keywords

solitonsnonlinear media

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (15)

Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method ⋮ A time-splitting Galerkin finite element method for the Davey-Stewartson equations ⋮ Soliton solutions of Davey-Stewartson equation by trial equation method and ansatz approach ⋮ Three different methods for new soliton solutions of the generalized NLS equation ⋮ Constructing two powerful methods to solve the Thomas-Fermi equation ⋮ Modulation instability, conservation laws and soliton solutions for an inhomogeneous discrete nonlinear Schrödinger equation ⋮ On the exact solutions to some system of complex nonlinear models ⋮ Some special solutions to the hyperbolic NLS equation ⋮ Galerkin methods for the Davey-Stewartson equations ⋮ A comparative study of numerical methods for solving the generalized Ito system ⋮ Bright, dark, and singular solitons in magneto-electro-elastic circular rod ⋮ Applicable symbolic computations on dynamics of small-amplitude long waves and Davey-Stewartson equations in finite water depth ⋮ New exact solutions and modulation instability for the nonlinear \((2+1)\)-dimensional Davey-Stewartson system of equation ⋮ New exact solutions of the Davey-Stewartson equation with power-law nonlinearity ⋮ Maximal thermo-geometric parameter in a nonlinear heat conduction equation

Cites Work

• The \(\frac{G'}{G}\) method and 1-soliton solution of the Davey-Stewartson equation
• Propagating wave patterns for the `resonant' Davey-Stewartson system
• Propagating wave patterns and ``peakons of the Davey-Stewartson system
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• The variational iteration method for solving linear and nonlinear systems of PDEs
• Ill-posedness for the nonlinear Davey-Stewartson equation
• Some special solutions of a generalized Davey-Stewartson system
• Long-wave short-wave resonance case for a generalized Davey-Stewartson system
• Closing the gap in the purely elliptic generalized Davey-Stewartson system
• The Cauchy problem for the elliptic-hyperbolic Davey-Stewartson system in Sobolev space
• Improvement of He's variational iteration method for solving systems of differential equations
• Variational iteration method -- some recent results and new interpretations
• Abundant families of Jacobi elliptic function solutions of the \((2+1)\)-dimensional integrable Davey-Stewartson-type equation via a new method
• Numerical simulation of the modified regularized long wave equation by He's variational iteration method
• The use of variational iteration method and homotopy perturbation method for solving two nonlinear equations
• Exact solutions to the combined KdV–mKdV equation by the extended mapping method
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS

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