In this paper, we find the exact solutions of some nonlinear evolution equations by using ( ′ G )expansion method. Four nonlinear models of physical significance i.e. the symmetric regularized longwave equation, the Klein-Gordon-Zakharov equations, the Burgers-Kadomtsev-Petviashvili equation and the nonlinear Schrödinger equation with a cubic nonlinearity are considered and obtained their exact...

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n, n) equation, Zakharov–Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM–Laplace–Pa...

Abstract. Very steep waves constitute an essentially nonlinear and complicated phenomenon. Inter-related experimental and theoretical efforts are thus required to gain a better understanding of their generation and propagation mechanisms. A nonlinear focusing process in which a single unidirectional steep wave emerges from an initially wide amplitudeand frequency-modulated wave group at a predi...

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solution...

We prove local well-posedness for the L2 critical generalized Zakharov-Kuznetsov equation in Hs, s∈(3/4,1). also that is “almost well-posedness” initial data u0∈Hs, s∈[1,2), sense solution belongs to a certain intersection C([0,T]:Hs(R3))∩XTs and unique within class, where we can ensure continuity of data-to-solution map an only slightly larger space. solutions satisfy expected conservation L2−...

We study a rather general class of optimal “ballistic” transport problems for matrix-valued measures. These naturally arise, in the spirit Brenier (Commun Math Phys 364(2):579–605, 2018), from certain dual formulation nonlinear evolutionary equations with particular quadratic structure reminiscent both incompressible Euler equation and Hamilton–Jacobi equation. The examples include ideal MHD, t...

The multi-component nonlinear Schrödinger equation related to C.I ' Sp(2p)/U(p) and D.III ' SO(2p)/U(p)-type symmetric spaces with non-vanishing boundary conditions is solvable with the inverse scattering method (ISM). As Lax operator L we use the generalized Zakharov-Shabat operator. We show that the ISM for the Lax operator L(x, λ) is a nonlinear analog of the Fourier-transform method. As app...