The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odin...The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schr¨odinger equation and its modified form are formally obtained.展开更多
By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions o...By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions of the new Hamiltonian am- plitude equation and the Ostrovsky equation, such as solitary wave solutions, kink and anti-kink wave solutions and periodic travelling wave solutions, are obtained, respectively.展开更多
文摘The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schr¨odinger equation and its modified form are formally obtained.
文摘By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions of the new Hamiltonian am- plitude equation and the Ostrovsky equation, such as solitary wave solutions, kink and anti-kink wave solutions and periodic travelling wave solutions, are obtained, respectively.
