Rational solution to a shallow water wave-like equation
نویسندگان
چکیده
منابع مشابه
The Exact Rational Solutions to a Shallow Water Wave-Like Equation by Generalized Bilinear Method
A Shallow Water Wave-like nonlinear differential equation is considered by using the generalized bilinear equation with the generalized bilinear derivatives 3,x D and 3,t D , which possesses the same bilinear form as the standard shallow water wave bilinear equation. By symbolic computation, four presented classes of rational solutions contain all rational solutions to the resulting Shallow Wat...
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Submitted: Nov 12, 2013; Accepted: Dec 18, 2013; Published: Dec 22, 2013 Abstract: In this article, we have employed an enhanced (G′/G)-expansion method to find the exact solutions first and then the solitary wave solutions of the nonlinear generalized shallow water wave equation. Here we have derived solitons, singular solitons and periodic wave solutions through the enhanced (G′/G)-expansion ...
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Two classes of rational solutions to a KdV-like nonlinear differential equation are constructed. The basic object is a generalized bilinear differential equation based on a prime number p 1⁄4 3. A conjecture is made that the two presented classes of rational solutions contain all rations solutions to the considered KdV-like equation, which are generated from polynomial solutions to the correspo...
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Majority of the hodograph transform solutions of the one-dimensional nonlinear shallow-water wave equations are obtained through integral transform techniques. This approach, however, might involve evaluation of elliptic integrals, which are highly singular. Here, we couple the hodograph transform approach with the classical eigenfunction expansion method rather than integral transform techniqu...
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and Applied Analysis 3 use the Kato theorem 29 to establish the local well-posedness for 1.5 with initial value u0 ∈ H with s > 3/2. Then, we present a precise blow-up scenario for 1.5 . Provided that u0 ∈ H R ⋂ L1 R and the potential y0 1−∂x u0 does not change sign, the global existence of the strong solution is shown to be true. Finally, under suitable assumptions, the existence and uniquenes...
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ژورنال
عنوان ژورنال: Thermal Science
سال: 2016
ISSN: 0354-9836,2334-7163
DOI: 10.2298/tsci1603875m