In this paper we establish the nonlinear stability of solitary travelling-wave solutions for the Kawahara-KdV equation ut + uux + uxxx − γ1uxxxxx = 0, and the modified Kawahara-KdV equation ut + 3u 2ux + uxxx − γ2uxxxxx = 0, where γi ∈ R is a positive number when i = 1, 2. The main approach used to determine the stability of solitary travelling-waves will be the theory developed by Albert in [1].

In this paper, we study the computability of the solution operator of the initial problem for the nonlinear Kawahara equation, which is based on the Type-2 Turing machines. We will prove that in Sobolev space 2 ( ) s H R , for 0 s ≥ , the solution operator: 2 : ( ) s R K H R → ( ; C R 2 ( )) s H R is ( ,[ s H δ ρ → ]) s H δ -computable. The conclusion enriches the theory of computability. Key w...

in this article, we apply the multiquadric radial basis function (rbf) interpo-lation method for nding the numerical approximation of traveling wave solu-tions of the kawahara equation. the scheme is based on the crank-nicolsonformulation for space derivative. the performance of the method is shown innumerical examples.

In this paper, we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiationmatrix and discrete Fourier transform. The relationship is crucial for implementing the scheme efficiently. By using the relationship, we can apply the Fast Fourier transform to solve the Kawahara equation. The effecti...

This article is concerned with the unconditional well-posedness for Kawahara equation on real line and shows that this holds true initial data in L 2 ( R ) . achieved by applying an infinite iteration scheme of normal form reductions.

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the (1 + 1) dimensional modified Kawahara equation by using the following two methods: (i) A further improved ( ′ G )expansion method, where G = G(ξ) satisfies the auxiliary ordinary differential equation [G′(ξ)]2 = aG2(ξ) + bG4(ξ) + cG6(ξ), where ξ = x − V t while a, b, c and V...