Dynamics of three nonisospectral nonlinear Schrödinger equations, 2019
Dynamics of three nonisospectral nonlinear Schrödinger equations (NNLSEs), following different ti... more Dynamics of three nonisospectral nonlinear Schrödinger equations (NNLSEs), following different time dependencies of the spectral parameter, are investigated. First, we discuss the gauge transformations between the standard nonlinear Schrödinger equation (NLSE) and its first two nonisospectral counterparts, for which we derive solutions and infinitely many conserved quantities. Then, exact solutions of the three NNLSEs are derived in double Wronskian terms. Moreover, we analyze the dynamics of the solitons in the presence of the nonisospectral effects by demonstrating how the shapes, velocities, and wave energies change in time. In particular, we obtain a rogue wave type of soliton solutions to the third NNLSE.
Dynamics of three nonisospectral nonlinear Schrödinger equations, 2019
Dynamics of three nonisospectral nonlinear Schrödinger equations (NNLSEs), following different ti... more Dynamics of three nonisospectral nonlinear Schrödinger equations (NNLSEs), following different time dependencies of the spectral parameter, are investigated. First, we discuss the gauge transformations between the standard nonlinear Schrödinger equation (NLSE) and its first two nonisospectral counterparts, for which we derive solutions and infinitely many conserved quantities. Then, exact solutions of the three NNLSEs are derived in double Wronskian terms. Moreover, we analyze the dynamics of the solitons in the presence of the nonisospectral effects by demonstrating how the shapes, velocities, and wave energies change in time. In particular, we obtain a rogue wave type of soliton solutions to the third NNLSE.
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