New exact wave solutions for Hirota equation

The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions

“…Subsequently, the multisolitons, breathers, rogue waves, and highorder rogue waves for the Hirota equation (1) were studied by many researchers via generalized Darboux transformation method and other methods [2][3][4][5][6]. For the integrability and other types of solutions of the Hirota model (1), we refer to [7][8][9]. The aim of this paper is to study the modified coupled Hirota equation in the following form [10]:…”

Dark and singular dispersive optical solitons of Schrödinger–Hirota equation by modified simple equation method

“…Dispersive optical solitons are studied when group velocity dispersion (GVD) is small and needs to be supplemented with third order dispersion (3OD) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The model that accuretely describes this phenomena is the Schrödinger-Hirota equation (SHE) which stems from the familiar nonlinear Schrödinger's equation (NLSE) through Lie transform.…”

Soliton solution in nonlinear lattice with nearest neighbour Born–Mayer interaction

“…The development of nonlinear differential equations are playing an increasingly important role in several areas of science in general and physics in particular. Some of the methods used for obtaining exact solutions of nonlinear equations are first integral method [1][2][3][4][5], the functional variable method [6,7], the expansion method [8], the direct algebraic method (DAM) [9,10], etc.…”