Fourth Order Nonlinear Evolution Equation For Interfacial Gravity Waves In The Presence Of Air Flowing Over Water And A Basic Current Shear [PDF]
International Journal of Applied Mechanics and Engineering, 2015 A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) is derived for gravity waves propagating at the interface of two superposed fluids of infinite depth ...
D.P. Majumder, A.K. Dhar
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, 2019 Nonlinear Evolution Equation presents state-of-the-art theories and results on nonlinear evolution equation, showing related mathematical methods and applications. The basic concepts and research methods of infinite dimensional dynamical systems are discussed in detail.
Chen, Fei +3 more
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Controllability for a Nonlinear Abstract Evolution Equation
Mathematical Notes, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rozanova A.V.
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Observations on the basic (G′/G)-expansion method for finding solutions to nonlinear evolution equations [PDF]
, 2010 The extended tanh-function expansion method for finding solutions to nonlinear evolution equations delivers solutions in a straightforward manner and in a neat and helpful form.
Parkes, E.J.
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Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. [PDF]
, 2012 The periodic KdV equation arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls in the phase space such that the Cauchy problem for KdV is well posed on the ...
Blower, Gordon
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Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method [PDF]
, 2009 The homotopy analysis method is applied to the short-pulse equation in order to find an analytic approximation to the known exact solitary upright-loop solution. It is demonstrated that the approximate solution agrees well with the exact solution.
Abbasbandy, S., Parkes, E.J.
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Multiscale expansion and integrability properties of the lattice potential KdV equation [PDF]
, 2008 We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schrödinger
Decio Levi +10 more
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Neumann problem on the semi-line for the Burgers equation [PDF]
, 2011 In this article, the Neumann problem on the semi-line for the Burgers equation is considered. The problem is reduced to a nonlinear integral equation in one independent variable, whose unique solution is proven to exist for small time.
Sommacal, Matteo, de Lillo, Silvana
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Comment on “Application of (G′/G)-expansion method to travelling-wave solutions of three nonlinear evolution equation" [Comput Fluids 2010;39;1957-63] [PDF]
, 2011 In a recent paper [Abazari R. Application of (G′ G )-expansion method to travelling wave solutions of three nonlinear evolution equation. Computers & Fluids 2010;39:1957–1963], the (G′/G)-expansion method was used to find travelling-wave solutions to ...
Parkes, Edward
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Representations of sl(2,?) in category O and master symmetries [PDF]
, 2015 We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such
J. P. Wang, Wang, Jing Ping
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