[PDF] Top 20 Existence and nonexistence of solutions for the generalized Camassa Holm equation

... Recently, Tian et al. [] investigated the well-posedness of the Cauchy problem and the scattering problem for equation (.), studied the problem of passing to the limit as α → , and obtained the scattering data ... See full document

... and generalized p-Laplacian which involves two different ...the existence and nonexistence of positive solutions for the fractional system are received, the impact of the two different ... See full document

... global existence and nonexistence of solutions for a quasilinear parabolic equation with null Dirichlet boundary ...global solutions including critical case, and we also give global ... See full document

... where t, x, μ ∈ R and u(t, x) ∈ R. Equation () can also be derived from the D water wave problem. For a degenerate case, Schneider and Eugene [] have proved that the long wave limit can be described ... See full document

... In order to prove the nonexistence of nontrivial solution of the problem 2.21, we use the test function method, which has been used in 25 and references therein. Some modification has been made in our proof. The ... See full document

... with a, λ , m > 0 and 1 < p < N. By variational methods we prove that problem (0.1) admits at least two solutions under appropriate assumptions on f (u) and h(x). The main difficulty to overcome is the lack ... See full document

... of solutions to a weakly dissipative generalized Camassa-Holm equation, which contains higher power nonlinear dispersion terms and a convection ...global existence result of the ... See full document

... the Camassa-Holm ...for Camassa-Holm equation, proving that the corresponding solution to ...the Camassa-Holm equation is identically zero whenever it vanishes on ... See full document

... the Camassa-Holm equation and other partial differential equations, the reader is referred to ...weak solutions for a generalized hyperelastic-rod wave equation (or a ... See full document

... (1.1), Holm [4] not only studied the effects of balance parameter a and kernel function of solitary wave structures but also investi- gated their interactions analytically with ε = 0 and numerically with small ... See full document

... The Camassa-Holm equation, a completely integrable evolution equation, contains rich geometric ...the existence of the bi-Hamiltonian structure and the so-called peaked wave ... See full document

... CH equation is a quadratic order water wave equation in an asymptotic expansion for unidirectional shallow water waves described by the incompressible Euler equations, which was found earlier by ... See full document

... and Holm equation () was derived through an asymp- totic expansion from the Hamiltonian of Euler’s equation in the shallow water ...The equation is an in- tegrable system and contains both ... See full document

... coupled Camassa-Holm ...of solutions in Section ...the existence of bounded random absorbing sets and the asymptotic compactness of the random dynamical system and prove the existence ... See full document

... a Generalized Fourier Transform. The generalized exponents are the squares of the eigenfunctions of the associated spectral ...the solutions u(x, t) are confined to be functions in the Schwartz ... See full document

... wave solutions for the generalized Camassa-Holm Equation ...fuzzy Camassa- Holm equation by using homtopy analysis ...wave solutions of (4) in the form of u ... See full document

... a generalized Camassa-Holm equation (gCH) with cubic ...peakon solutions. We then prove that the peakons for the gCH equation are orbitally stable by using the method of ... See full document

... the existence and uniqueness of global strong solutions, global weak solutions and the exponential asymptotical stabilization of solutions to the ...of solutions to the transport ... See full document

... wave solutions for a class of nonlinear fourth order variant of a generalized Camassa-Holm equation, ...wave solutions for a class of generalized kdv equation, ... See full document

... soliton solutions with multiple peaks for ...the Camassa-Holm and Degasperis-Procesi equations (see ...Novikov equation with a peak ...Novikov equation associated with the initial value ... See full document