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In this paper, we use the generalized tanh method to obtain exact solutions for a class of fifth-order nonlinear systems. A particular case is given by the integrable Mikhailov-Novikov-Wang system (MNW). Periodic and solitons solutions are formally derived. The Mathematica is used.
The Cole-Hopf transform is used to construct exact solutions to a generalization of both the seventh-order Lax KdV equation Lax KdV7 and the seventh-order Sawada-Kotera-Ito KdV equation Sawada-Kotera-Ito KdV7.
The tanh-coth method is used to seek solutions to obtain solutions to the new integrable sixth-order Korteweg-de Vries equation (KdV6). Following the analogy between the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (MKdV) we construct a new system equivalent to KdV6 from which exact solutions to original equation and derived,… (More)
mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Using the idea of the very recently generalized Kudryashov method and based on a generalized Riccati equation we present an alternative method which can be considered as an extension of the well known… (More)
Low-lying states of an ion-molecular D þ 2 complex in quantum rings with different and small cross-sections are analyzed. Following the adiabatic procedure, we have deduced a one-dimensional wave equation with periodic conditions, which describes low-lying levels related to the electron rotation around the symmetric axis under the Coulomb interaction with… (More)