Comparison Between the Exact Solutions of Three Distinct Shallow Water Equations Using the Painlevé Approach and Its Numerical Solutions

DOI10.20537/nd200305zbMath1455.35038OpenAlexW3090673235MaRDI QIDQ5143174

Ahmet Bekir, Emad H. M. Zahran, Maha S. M. Shehata

Publication date: 11 January 2021

Published in: Nelineinaya Dinamika (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/nd722

zbMATH Keywords

Camassa-Holm equationNovikov-Veselov equation\((3 + 1)\)-dimensional Kadomtsev-Petviashvili (KP) equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems for nonlinear higher-order PDEs (35G25) Exact solutions to problems in general relativity and gravitational theory (83C15) Traveling wave solutions (35C07) Soliton solutions (35C08) Fractional partial differential equations (35R11)

Related Items (2)

New analytic solutions for fluid flow equations in higher dimensions around an offshore structure describing bidirectional wave surfaces ⋮ Symbolically computing the shallow water via a \((2+1)\)-dimensional generalized modified dispersive water-wave system: similarity reductions, scaling and hetero-Bäcklund transformations

Cites Work

• Well-posedness and persistence properties for the Novikov equation
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• The variational iteration method for analytic treatment for linear and nonlinear ODEs
• Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation
• Wave breaking for nonlinear nonlocal shallow water equations
• New explicit solitary wave solutions for \((2+1)\)-dimensional Boussinesq equation and \((3+1)\)-dimensional KP equation
• Wave breaking for the stochastic Camassa-Holm equation
• Explicit solutions of the Camassa-Holm equation
• A note on the Cauchy problem of the Novikov equation
• The Camassa--Holm Equation and The String Density Problem
• Global weak solutions for the Novikov equation
• The Periodic Cauchy Problem for Novikov's Equation
• Generalizations of the Camassa–Holm equation
• An integrable shallow water equation with peaked solitons
• The Cauchy problem for the Novikov equation
• Unnamed Item

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