Nikolay A. Kudryashov, Chao-Qing Dai, Qin Zhou, Daniil R. Nifontov
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Painlevé analysis, conservation laws and exact solutions of the fourth-order nonlinear Schrödinger equation
The fourth-order nonlinear Schrödinger equation for describing optical solitons is studied. The Painlevé test for nonlinear partial differential equations is used to study integrability properties of equation. It is shown that the equation does not pass the Painlevé test and consequently the Cauchy problem cannot be solved by the inverse scattering transform. A condition is found for the parameter value of the equation at which an analytical solution is possible in traveling wave variables. Using direct algebraic transformations of the system of equations, three independent conservation laws are constructed for the equation under study. The first integrals of the reduction to the nonlinear ordinary differential equation are obtained from the conservation laws. Optical solitons described by the partial differential equation are found under additional conditions on the parameters of the equation. Conserved densities corresponding to the power, linear momentum, and energy of optical solitons are calculated.
期刊介绍：
The aims of this peer-reviewed online journal are to distribute and archive all relevant material required to document, assess, validate and reconstruct in detail the body of knowledge in the physical and related sciences.
The scope of EPJ Plus encompasses a broad landscape of fields and disciplines in the physical and related sciences - such as covered by the topical EPJ journals and with the explicit addition of geophysics, astrophysics, general relativity and cosmology, mathematical and quantum physics, classical and fluid mechanics, accelerator and medical physics, as well as physics techniques applied to any other topics, including energy, environment and cultural heritage.
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