The manuscript solves a modified Kawahara equation (mKE) within two cases with and without damping term by applying the Laplace homotopy perturbation method (LHPM). Since damped mKE is non-integrable (i.e., it does not have analytic integrals) exact initial conditions, this challenge makes many numerical methods fail to solve equations. In article, we suggested new modification at LHPM setting ...

Utilizing of illustrative scheming programming, the study inspects careful voyaging wave engagements from nonlinear time fractional modified Kawahara equation (mKE) by employing advanced exp − φ ξ -expansion policy in t...

Hajime Kawahara, Kohji Yoshikawa, Shin Sasaki, Yasushi Suto, Nobuyuki Kawai, Kazuhisa Mitsuda, Takaya Ohashi, and Noriko Y. Yamasaki 1Department of Physics, School of Science, The University of Tokyo, Tokyo 113-0033 [email protected] 2Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397 3Department of Physics, Tokyo Institute of Techn...

In a previous paper we proved that long-wavelength solutions of the waterwave problem in the case of zero surface tension split up into two wave packets, one moving to the right and one to the left, where each of these wave packets evolves independently as a solution of a Korteweg-de Vries (KdV) equation. In this paper we examine the effect of surface tension on this scenario. We find that we o...

Hajime Kawahara, Kohji Yoshikawa, Shin Sasaki Yasushi Suto, Nobuyuki Kawai, Kazuhisa Mitsuda, Takaya Ohashi, and Noriko Y. Yamasaki 1Department of Physics, School of Science, The University of Tokyo, Tokyo 113-0033 [email protected] 2Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397 3Department of Physics, Tokyo Institute of Techno...

In this paper, we examined the approximations to time-fractional Kawahara equation and modified equation, which model creation of nonlinear water waves in long wavelength area transmission signals. We implemented two novel techniques, namely homotopy perturbation transform method Elzaki decomposition method. The derivative having fractional-order is taken Caputo sense. Adomian He’s polynomials ...

We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto–Sivashinsky (KS) equation with an additional nonlocal term that contains stabilizing/destabilizing and dispersive parts. As for the local generalized Kuramoto–Sivashinsky (gKS) equation (see, e.g., [T. Kawahara and S. Toh, Phys. Fluids, 31 (1988), pp. 2103–2111]), we sho...

We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.