modified Korteweg-de Vries solitons
Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation
... admit solitons and some of these theoretical equations are also responsible for the experimental discovery of solitons ...like solitons, but e.g. dispersion- managed solitons, rogue waves, ...
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Application of Petrov-Galerkin finite element method to shallow water waves model: Modified Korteweg-de Vries equation
... equation with a very popular and eective numerical scheme. This is the cubic B-spline Petrov-Galerkin method. The topics covered in this paper are linear stability analysis, the dynamics of single solitary wave of mKdV ...
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Some traveling wave solutions of soliton family
... or solitons. Solitons are self-localized wave packets arising from a robust balance between dispersion and ...like Korteweg-de Vries (KdV) or modified Korteweg-de ...
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Low frequency analogue Hawking radiation: the Korteweg–de Vries model
... We derive analytic expressions for the low-frequency properties of the analogue Hawking radiation in a general weak-dispersive medium. A thermal low-frequency part of the spectrum is expected even when dispersive effects ...
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Martingale Solution to Stochastic Extended Korteweg de Vries Equation
... In this paper, we consider the stochastic extended Korteweg-de Vries equation with multiplicative random noise. We prove the existence of martingale solution to stochastic KdV2 equation driven by ...
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Remark on the well-posedness of weakly dispersive equations
... Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle , Commun.. Klein, and J.C.[r] ...
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Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain
... [29] Russell, D. L, D. L. Computational study of the Korteweg-de Vries equation with localized control action, Distributed Parameter Control Systems: New Trends and Applications, G. Chen, E. B. Lee, ...
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Existence and stability of solitary waves for the generalized Korteweg-de Vries equations
... fractional Korteweg-de Vries equations with general ...generalized Korteweg-de Vries equations under some assumptions of the nonlinear ...
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Multi solitons solutions of Korteweg de Vries (KdV) equation : six solitons
... In year 1895, John Scott Russell‟s theoretical understanding has been studied by Diederik Johannes Korteweg and his PhD student, Gustav de Vries. They have derived an equation that related with John ...
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PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
... Abstract: We discuss several PT -symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT -symmetric defor- mations of the supersymmetric ...
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The Korteweg de Vries equation and a Diophantine problem related to Bernoulli polynomials
... Pint?r and Tengely Advances in Difference Equations 2013, 2013 245 http //www advancesindifferenceequations com/content/2013/1/245 R ES EA RCH Open Access The Korteweg de Vries equation and a Diophant[.] ...
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Hyperbolic Tangent ansatz method to space time fractional modified KdV, modified EW and Benney–Luke Equations
... +2D β x u(x, t)D xt βα u(x, t) = 0 (3) is considered as the last equation to be solved exactly, where x > 0, t > 0 and µ and η are positive parameters, linked to the inverse bond number, whose characteristics is to ...
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An Unconventional Splitting for Korteweg de Vries-Burgers Equation
... u(−15, t ) = u(15, 0) = 0, t > 0. (27) We take ǫ = 1.0 and consider for µ the set of parameters µ = 0.04, 0.01, 0.001, 0.0005 and run the simulation up to time t = 12 with ∆t = 0.03, h = 0.02. The results are shown in ...
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PT-symmetric deformations of the Korteweg-de Vries equation
... Abstract: We propose a new family of complex PT -symmetric extensions of the Korteweg-de Vries equation. The deformed equations can be associated to a sequence of non-Hermitian Hamiltonians. The ...
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The Pfaffian Technique: A (2 + 1) Dimensional Korteweg de Vries Equation
... The (2 + 1)-dimensional Korteweg de Vries (KdV) equation, which was first derived by Boiti et al ., has been studied by various distinct methods. It is known that this (2 + 1)-dimensional KdV ...
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Well posedness of Korteweg De Vries Burgers equation on a Finite Domain
... In this paper,we consider the Korteweg-de Vries-Burgers equation on a finite domain with initial value and nonhomogeneous boundary conditions. This particular problem arises in the theory of ...
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Computational analysis of shallow water waves with Korteweg-de Vries equation
... In this paper, the collocation nite element method based on quintic B-spline functions is suc- cessfully applied to the generalized KdV equation to examine the motion of a single solitary wave whose analytical solution ...
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Conservation laws for a generalized Ito-type coupled KdV system
... In this paper, the conservation laws for a generalized Ito-type coupled Korteweg-de Vries (KdV) system are constructed by increasing the order of the partial differential equations. The generalized ...
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Nonlinear mechanism of tsunami wave generation by atmospheric disturbances
... forced Korteweg-de Vries equation described the wave generation by the moving atmo- spheric disturbance are given in the paper by Akylas (1984) and the following papers cited by Grimshaw et ...of ...
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Chebyshev Rational Approximations for the Rosenau-KdV-RLW Equation on the Whole Line
... This section addresses the basic notions and working tools concerning orthogonal modified Chebyshev rational functions. More specifically, it presents some properties of the modified Chebyshev rational ...
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