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 discuss commuting flows and conservation laws for Lax hierarchies on noncommutative spaces in the framework of the Sato theory. On commutative spaces, the Sato theory has revealed essential aspects of the integrability for wide class of soliton equations which are derived from the Lax hierarchies in terms of pseudo-differential operators. Noncommutative extension of the Sato theory has been ...

By using gauge transformations, we manage to obtain new solutions of (2+1)-dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and Sawada-Kotera(SK) equations from non-zero seeds. For each the preceding equations, a Galilean type transformation between these $u_2$ previously known $u_2^{\prime}$ generated zero seed is given. We present several explicit formulas single-soliton for $u_2...

In this paper, a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system is investigated in fluid mechanics via the symbolic computation. With help of Hirota method, we derive some singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on finite difference get numerical one-soliton We graphically show shock-wave solutions, observe that solutions are explosive unsta...

Abstract A Generalized (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation (2D- gCDGKSE) is an integro-differential that describes tow-layer fluid interaction. The non-autonomous gCDGKSE (NAUT-gCDGKSE) was rarely considered in the literature. In previous works, concepts of two-layer interaction and non-uniform were not explored. This motivated us to focus attention on these themes. Our...