Abstract
Propagating modes in a class of nonic derivative nonlinear Schrödinger equations incorporating ninth order nonlinearity are investigated by the method of dynamical systems. Because the functions [Formula: see text] and [Formula: see text] in the solutions [Formula: see text], [Formula: see text] satisfy a four-dimensional integral system having two first integrals (i.e. the invariants of motion), a planar dynamical system for the squared wave amplitude [Formula: see text] can be derived in the invariant manifold of the four-dimensional integrable system. By using the bifurcation theory of dynamical systems, under different parameter conditions, bifurcations of phase portraits and exact periodic solutions, homoclinic and heteroclinic solutions for this planar dynamical system can be given. Therefore, under some parameter conditions, solutions [Formula: see text] and [Formula: see text] can be exactly obtained. Thirty six exact explicit solutions of equation are derived.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.