Interactions between butterfly-shaped pulses in the inhomogeneous media

Breathers and localized solutions of complex modified Korteweg–de Vries equation

“…So the breathers are Akhmediev breathers. 7,8 When the parameters satisfy the condition |β 2 1 − 4k 2 | → 0, the localized solutions in the time and space coordinates also be shown in Fig. 2(b).…”

“…[1][2][3][4][5] Those models can often be described by soliton equations, such as Korteweg-de Vries (KdV) equation, modified Korteweg-de Vries (mKdV) equation, nonlinear Schrödinger (NLS) equation, sine-Gordon (SD) equation and variable coefficients equations. [6][7][8][9][10][11][12] The analytical calculations of those soliton equations have been in the limelight in the research of the nonlinear science. [13][14][15][16][17][18][19][20][21][22][23] Currently, several powerful mathematical methods have been applied to solve the exact solution in the theory of solitons, such as the Darboux transformation (DT), inverse scattering method, Backlund transformation and the bilinear derivative method.…”

Higher-order-effects management of soliton interactions in the Hirota equation

“…Therefore, in this paper, we are devoted to investigate the interaction between two solitons described by the Hirota equation via the bilinear method. Generally speaking, the interaction force between two solitons can be repulsive or attractive, depending mainly on their relative phase [11,18,19]. Soliton interactions can be used in pulse compression, energy conversion, and amplification [20][21][22].…”

Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium

“…The incoherently coupled vector soliton means that the coupling is phase insensitive, and the incoherently CNLS systems have been well investigated in Refs. [9,10]. As a special incoherently CNLS system, the Manakov system has the following structure [11]:…”

“…During the past decades, considerable research interest has been focused on the nonlinear Schrödinger (NLS) equation, which describes the propagation of optical solitons in a mono-mode fiber for the scalar field [1][2][3][4][5][6][7][8][9][10][11][12], and the principle of such scalar NLS soliton is R. Guo based on the balance between the group velocity dispersion (GVD) and self-phase modulation (SPM) [1]. In view of the nonlinear phase change resulting from the cross-phase modulation(XPM) in the birefringent fibers or multi-mode fibers, one must consider interactions of several field components at different frequencies or polarizations, and the dynamic features of such solitons are usually governed by the coupled nonlinear Schrödinger (CNLS) systems [1].…”