A new transformation v=4(lnf)xx that can formulate a quintic linear equation and pair of Hirota’s bilinear equations for the (2 + 1)-dimensional Sawada–Kotera (2DSK) Eq. (1) or u=4(lnf)x 2DSK (2) is reported firstly, which enables one to obtain set multiple soliton solutions equation. They are not special cases known solitons. The results presented in this paper show only possesses two sets sol...

This study investigates the wave solutions of time-fractional Sawada–Kotera–Ito equation (SKIE) that arise in shallow water and many other fluid mediums by utilizing some most flexible high-precision methods. The SKIE is a nonlinear integrable partial differential (PDE) with significant applications dynamics mechanics. However, traditional numerical methods used for analyzing this are often pla...

The main purpose of this research is to propose a new methodology observe class time-fractional generalized fifth-order Korteweg–de Vries equations. Laplace transform along with homotopy perturbation algorithm utilized for the solution and analysis in current study. This extended technique provides improved convergent series solutions through symbolic computation. proposed applied Sawada–Kotera...

E. Abouzaid, M. Arenton, A.R. Barker, ∗ L. Bellantoni, E. Blucher, G.J. Bock, E. Cheu, R. Coleman, M.D. Corcoran, B. Cox, A.R. Erwin, C.O. Escobar, A. Glazov, A. Golossanov, R.A. Gomes, P. Gouffon, Y.B. Hsiung, D.A. Jensen, R. Kessler, K. Kotera, A. Ledovskoy, P.L. McBride, E. Monnier, † H. Nguyen, R. Niclasen, D.G. Phillips II, E.J. Ramberg, R.E. Ray, M. Ronquest, E. Santos, W. Slater, D. Smit...

With the advantages of fast calculating speed and high precision, physics-informed neural network method opens up a new approach for numerically solving nonlinear partial differential equations. Based on conserved quantities, we devise two-stage PINN which is tailored to nature equations by introducing features physical systems into networks. Its remarkable advantage lies in that it can impose ...

We consider the solution of spectral problems with elliptic coefficients in the framework of the Hermite ansatz. We show that the search for exactly solvable potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gröbner bases method and others. New potentials and corresponding solutions of the Sawada–Kotera, Kaup– Kupershmidt, Boussinesq eq...

Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable Hénon-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivativ...