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This paper obtains the shock wave solution, also known as topological 1-soliton solution, of the Benney-Luke equation. The ansatz method is going to be used ...

Solitons and other solutions to Gardner equation by similarity
The similarity reductions and similarity solutions for the Gardner equation are ..... A. Yildirim, T. Hayat, O.M. Aldossary, A. Biswas, Shock Wave Solution of the Benney-. Luke Equation, Romanian Journal of Physics 57 (7–8), 1029–1034 ( 2012).

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Key words: KdV–Burgers equation with forcing term, Extended tanh method, ... travelling wave solution to the KdV-Burgers equation has been studied ..... H. Triki, A. Yildirim, T. Hayat, O.M. Aldossary, A. Biswas, Shock wave solution of the Benney–. Luke equation, Romanian Journal of Physics 57, 1029–1034 (2012). 16.

Department of Applied Mathematics 2011 Annual Report
Nonlinear Waves Seminar. Complex and .... Equations, Solutions, Nonlinear Waves. Jerrold Bebernes ..... Refined stability for gas-dynamic shocks ..... Benney -Luke equation”, Journal of Physics A: Mathematical and Theoretical, vol. 44, pg.

General solution of a special class of nonlinear BBM-B equation by
travelling wave solutions of nonlinear BBM-B equation when g(u) = e±u. 2. ..... Houria Triki, Ahmet Yildirim, T. Hayat, Omar M. Aldossary & Anjan Biswas, Shock wave solution of the Benney-Luke equation, Romanian Journal of Physics 57(7-8 ), ...

Mar 25, 2013 ... Gennady El, AWhitham equations and dispersive shock wavesA .... solitary wave solutions of the vector nonlinear Schrödinger equation .... 34B" 567 64 3( 77Conservation laws and web solutions for the Benney Luke equation.

A PseudoSpectral Procedure for the Solution of Nonlinear Wave
Sep 26, 2015 ... OF NONLINEAR WAVE EQUATIONS WITH EXAMPLES .... for the numerical solution of a broad class of nonlinear waves. ..... oblique shock reflection. .... [2] D. J. Benney and J. C. Luke, Interactions of permanent waves of ...

Key words: (2+1)-dimensional Gardner equation; Hirota bilinear method; multiple kink ..... H. TRIKI et al., Shock wave solution of Benney-Luke equation, Rom.

International Conference Nonlinear Waves in Fluids (dedicated to
Sep 14, 2012 ... waves asymptotic reductions can be readily obtained such as the Benney-Luke ( BL) .... equation, which is not asymptotically close to a solution of the .... device is left on dry land, a second wave may act as a shock on the plate ...

Modification of Truncated Expansion Method for Solving Some
solutions of the Konopelchenko-Dubrovsky equation the (n+1)-dimensional combined sinh- cosh-Gordon equation ... method presents a wider applicability for handling nonlinear wave equations. Keywords: Modification ...... Shock wave solution of Benney-Luke equation, Romanian Journal of Physics, Vol. 57, No. (7- 8), pp.
01_Mirzazadeh AAM-R535-MM-082612 Vol_7_Issue_2_December_2012.pdf

Dispersive shock wave interactions and two-dimensional ocean-wave ... asymptotic solution of the KdV equation for general step-like data is a single- ...... dates back to 1970 (Ablowitz and Benny, 1970); multiphase Whitham equations were.

Nonlinear Evolution Equations and Wave Phenomena - Software
Apr 3, 2015 ... Nonlinear Evolution Equations and Wave Phenomena: ..... 10:55 – 11:20 Min Chen: Solutions of Boussinesq systems .... Jinghua Yao, Kevin Zumbrun: O(2) Hopf bifurcation of viscous shock waves in a channel ..... 2:05 – 2:30 Shubin Wang: The Cauchy problem for generalized Benney-Luke equation.

View - OhioLINK Electronic Theses and Dissertations Center
equation. We find an orbital instability of a solitary wave solution due to the ...... can also derive the Benney-Luke equation with respect to the velocity ..... The Mach reflection phenomenon was first recognized as a characteristic of shock waves ...

A generalized Kudryashov method to some nonlinear evolution
Exact solutionsGeneralized Kudryashov methodSymbolic ... Step 1: To look for the traveling wave solution of equation, we take traveling wave ...... Akter, J., Akbar, M.A.: Exact solutions to the Benney–Luke equation and the ... Wang, G.-W. , Xu, T.-Z., Abazari, R., Jovanoski, Z., Biswas, A.: Shock waves and other solutions to ...

Runge-Kutta Integration of the Equal Width Wave Equation Using
Jan 8, 2015 ... The equal width (EW) equation governs nonlinear wave phenomena like ...... “ Shock wave solution of Benney-Luke equation,” Romanian.

An Extended Auxiliary Function Method and Its Application in mKdV
Feb 22, 2013 ... traveling wave solutions for nonlinear partial differential equations. ...... “Shock wave solution of Benney-Luke equation,” Romanian. Journal of ...

Hamiltonian Structure of Modulation Equations for Sine-Gordon
We call this family of solutions the “N-phase, quasiperiodic waves.” When ... wave equations, [Whitham (1974)] derived the modulation equations for slowly ... traveling wave was given later by [Luke (1966)]. This construction was extended to the multiphase case by [Ablowitz and Benney (1970)]. ... smoothing of shocks.

[email protected] 520.626.4885 - Department of
Grandchildren: Luke (8), Tony (6), Georgina (5), Jack (4), Alan (2). .... Developed (with Benney) consistent derivation of wave turbulence closure relying on minimal a ..... An Exact Solution for a Derivative Nonlinear Schrödinger Equation, Journal of ..... Shock bowing and vorticity dynamics during propagation into different ...

Three-Dimensional Long Water-Wave Phenomena - Annual Reviews
periodic-wave solutions (cnoidal waves) of the KdV equation. Further more .... by, among others, Benney & Luke (1964), Byatt-Smith (1971), Satsuma. (1976) ...

On the relevance of the dam break problem in the context of
Feb 9, 2010 ... he obtained a closed-form solution using a kinematic wave approximation. .... Equations (5), (6) can be also derived from Luke's Lagrangian ..... [13] D.J. Benney. .... of Conservation Laws and the Mathematical Theory of Shock.

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