In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. The N-order rational solution is derived by the it...In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. The N-order rational solution is derived by the iterative rule and it can be expressed by the determinant form. In particular, I calculate first-order and second-order rational solutions and obtain their figures according to different parameters.展开更多
The derivations of several conservation laws of the generalized nonlocal nonlinear Schrodinger equation are presented. These invaxiants are the number of particles, the momentum, the angular momentum and the Hamiltoni...The derivations of several conservation laws of the generalized nonlocal nonlinear Schrodinger equation are presented. These invaxiants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.展开更多
The Darboux transformation (DT) method is studied in a lot of local equations, but there are few of work to solve nonlocal equations by DT. In this letter, we solve the nonlocal nonlinear Schrödinger equation...The Darboux transformation (DT) method is studied in a lot of local equations, but there are few of work to solve nonlocal equations by DT. In this letter, we solve the nonlocal nonlinear Schrödinger equation (NNLSE) with the self-induced PT-symmetric potential by DT. Then the N-fold DT of NNLSE is derived with the help of the gauge transformation between the Lax pairs. Then we derive some novel exact solutions including the bright soliton, breather wave soliton. In particularly, the dynamic features of one-soliton, two-soliton, three-soliton solutions and the elastic interactions between the two solitons are displayed.展开更多
In this paper, we construct the Darboux transformation(DT) for the reverse-time integrable nonlocal nonlinear Schrodinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero see...In this paper, we construct the Darboux transformation(DT) for the reverse-time integrable nonlocal nonlinear Schrodinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions.Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula.展开更多
基金supported by the Shanghai Leading Academic Discipline Project under Grant No.XTKX2012by the Natural Science Foundation of Shanghai under Grant No.12ZR1446800,Science and Technology Commission of Shanghai municipalityby the National Natural Science Foundation of China under Grant Nos.11201302 and11171220.
文摘In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. The N-order rational solution is derived by the iterative rule and it can be expressed by the determinant form. In particular, I calculate first-order and second-order rational solutions and obtain their figures according to different parameters.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10474023 and 10674050） and Specialized Research Fund for the Doctoral Program of Higher Education （Grant No 20060574006）.
文摘The derivations of several conservation laws of the generalized nonlocal nonlinear Schrodinger equation are presented. These invaxiants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.
基金supported by the Natural Science Foundation of Liaoning Province,China(Grant No.201602678).
文摘The Darboux transformation (DT) method is studied in a lot of local equations, but there are few of work to solve nonlocal equations by DT. In this letter, we solve the nonlocal nonlinear Schrödinger equation (NNLSE) with the self-induced PT-symmetric potential by DT. Then the N-fold DT of NNLSE is derived with the help of the gauge transformation between the Lax pairs. Then we derive some novel exact solutions including the bright soliton, breather wave soliton. In particularly, the dynamic features of one-soliton, two-soliton, three-soliton solutions and the elastic interactions between the two solitons are displayed.
基金supported by the National Natural Science Foundation of China(Grant No.11771151)the Guangzhou Science and Technology Program of China(Grant No.201904010362)the Fundamental Research Funds for the Central Universities of China(Grant No.2019MS110)。
文摘In this paper, we construct the Darboux transformation(DT) for the reverse-time integrable nonlocal nonlinear Schrodinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions.Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula.
