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We show that all meromorphic solutions of the stationary reduction of the real cubic Swift-Hohenberg equation are elliptic or degenerate elliptic. We then obtain them all explicitly by the subequation method, and one of them appears to be a new elliptic solution.
Lie point symmetries of the 2+1-dimensional cubic Schrodinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable t
Axisymmetric and nonaxisymmetric patterns in the cubic-quintic Swift-Hohenberg equation posed on a disk with Neumann boundary conditions are studied via numerical continuation and bifurcation analysis. Axisymmetric localized solutions in the form of
In this paper, we consider the real modified Korteweg-de Vries (mKdV) equation and construct a special kind of breather solution, which can be obtained by taking the limit $lambda_{j}$ $rightarrow$ $lambda_{1}$ of the Lax pair eigenvalues used in the
We try to obtain meromorphic solution of Time dependent Schroedinger equation which partially satisfies Painleve Integrable property. Our study and analysis exhibits meromorphic behavior of classical particle trajectory. In other words, particle is c
A new variant of the $(2+1)$-dimensional [$(2+1)d$] Boussinesq equation was recently introduced by J. Y. Zhu, arxiv:1704.02779v2, 2017; see eq. (3). First, we derive in this paper the one-soliton solutions of both bright and dark types for the extend