in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

In this work, the dispersive shock wave (DSW) solution of a Boussinesq Benjamin–Ono (BBO) equation, standard equation with dispersion replaced by nonlocal dispersion, is derived. This DSW derived using two methods, fitting and from simple Whitham modulation equations for BBO equation. The first these yields edges DSW, while second complete solution. As could not be set in Riemann invariant form...

We study certain similarity solutions of the Benjamin-Ono-Burgers (BOB) equation and their role in the asymptotic behavior of the general solution. For small initial data in L 1 (R) we prove that a solution of the BOB equation exists in BC(R + ; L 1 (R)) and depends continuously on its initial data. Results about existence, uniqueness, regularity, and spatial asymptotics of solutions of a simil...

The regularized Benjamin–Ono equation appears in the modeling of long-crested interfacial waves in two-fluid systems. For this equation, Fourier–Galerkin and collocation semi-discretizations are proved to be spectrally convergent. A new exact solution is found and used for the experimental validation of the numerical algorithm. The scheme is then used to study the interaction of two solitary wa...

In recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. One such method is known as the new extended (G'/G)-expansion method and was proposed by Roshid et al. In this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (NLPDEs), namely the Benjamin-Ono equation. It is est...

Blow up and instability of solitary wave solutions to a generalized Kadomtsev– Petviashvili equation and two-dimensional Benjamin–Ono equations BY JIANQING CHEN*, BOLING GUO AND YONGQIAN HAN School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, People’s Republic of China Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, Peopl...