In this paper, numerical solution of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is obtained by using the mesh-free method based on the collocation method with radial basis functions (RBFs). Stability analysis of the method is discussed. The method is applied to several examples and accuracy of the method is tested in terms of $L_2$ and $L_infty$ error norms.

this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

We prove that the generalized Benjamin-Ono equations ∂tu + H∂2 xu ± u ∂xu = 0, k ≥ 4 are locally well-posed in the scaling invariant spaces Ḣsk(R) where sk = 1/2 − 1/k. Our results also hold in the nonhomogeneous spaces Hsk(R). In the case k = 3, local well-posedness is obtained in Hs(R), s > 1/3.

A bilinear estimate in Fourier restriction norm spaces with applications to the Cauchy problem ut − |D| αux + uux = 0 in (−T, T ) × R u(0) = u0 is proved, for 1 < α < 2. As a consequence, local well-posedness in H(R) ∩ Ḣ(R) follows for s > − 3 4 (α − 1) and ω = 1/α − 1/2 This extends to global well-posedness for all s ≥ 0.

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg–de Vries-type ut + uux − Mux = 0, with M being a general pseudodifferential operator and where p ≥ 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obta...