The Jimbo-Miwa equation (JME) that describes certain interesting (3+1)-dimensional waves in plasma physics is studied this work. Hirota bilinear developed via the Cole-Hopf transform. Then, symbolic computation, together with ansatz function schemes, are utilized to seek exact solutions. Some new solutions, such as multi-wave complexiton solution (MWCS), (MWS) and periodic lump (PLS), successfu...

The procedure of constructing linear ansatzes is algorithmized. Some exact solutions of a generalized complex Euler equation for a vector field, invariant under subalgebras of the Poincaré algebra AP (1, 3) are found. In this article, we consider the equation ∂Σk ∂x0 +Σl ∂Σk ∂xl = 0, Σk = Ek + iHk (k, l = 1, 2, 3). (1) It was proposed by W. Fushchych [1] to describe vector fields. This equation...

We present a succinct way of obtaining all possible higher dimensional generalization of Quantum Yang-Baxter Equation (QYBE). Using the scheme, we could generate the two popular three-simplex equations, namely: Zamolodchikov’s tetrahedron equation (ZTE) and Frenkel and Moore equation (FME). E-mail address: [email protected] E-mail address: [email protected] The Quantum Yang-Baxter Equation (Q...

The KP equation, which is an integrable nonlinear evolution equation in 2 + 1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the...