Fractional Sub-equation Method and Analytical Solutions to the Hirota-satsuma Coupled KdV Equation and Coupled mKdV Equation
نویسندگان
چکیده
منابع مشابه
Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation
and Applied Analysis 3 Theorem 5. If u(x, t) = f(x)g(t), function f(x) = xh(x), where λ > −1 and h(x) has the generalized Taylor series expansion h(x) = ∑∞ n=0 a n (x − x 0 ) αn, (i) β < λ + 1 and α arbitrary, or (ii) β ≥ λ+1, α arbitrary, and a n = 0 for n = 0, 1, . . . , m− 1, wherem − 1 < β ≤ m, then the generalized differential transform (8) becomes U α,β (k, h) = 1 Γ (αk + 1) Γ (βh + 1) [D...
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In this paper, we consider multi-component generalizations of the Hirota–Satsuma coupled Korteweg–de Vries (KdV) equation. By introducing a Lax pair, we present a matrix generalization of the Hirota–Satsuma coupled KdV equation, which is shown to be reduced to a vector Hirota–Satsuma coupled KdV equation. By using Hirota's bilinear method, we find a few soliton solutions to the vector Hirota–Sa...
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Article history: Received 28 January 2011 Received in revised form 28 March 2011 Accepted 22 April 2011 Available online 29 April 2011 Communicated by R. Wu
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Here, an analytic technique, namely the homotopy analysis method (HAM), is applied to solve a generalized Hirota–Satsuma coupled KdV equation. HAM is a strong and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations. Comparison of the results with those of Adomian’s decomposition method (ADM) and homotopy perturbation method (HPM), has led us to s...
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Collocation method using quintic B-splines finite element have been developed for solving numerically the HirotaSatsuma coupled MKdV equation. Accuracy of the proposed method is shown numerically by calculating conservation laws, 2 L and L norms on studying of a soliton solution. It is shown that the collocation scheme for solutions of the MKdV equation gives rise to smaller errors and is qui...
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ژورنال
عنوان ژورنال: British Journal of Mathematics & Computer Science
سال: 2014
ISSN: 2231-0851
DOI: 10.9734/bjmcs/2014/7059