Self-Consistent Sources and Conservation Laws for Nonlinear Integrable Couplings of the Li Soliton Hierarchy

Abstract

New explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Li soliton hierarchy are obtained. Then, the nonlinear integrable couplings of Li soliton hierarchy with self-consistent sources are established. Finally, we present the infinitely many conservation laws for the nonlinear integrable coupling of Li soliton hierarchy.

The generalized fractional trace variational identity and fractional integrable couplings of Kaup-Newell hierarchy

“…The fractional analysis has attracted the interest of many researchers, because fractional analysis has numerous applications: kinetic theories, 1, 2 statistical mechanics, 3,4 dynamics in complex media, 5, 6 and many others. [7][8][9][10][11][12] The main advantage of fractional derivative in comparison with classical integer-order models is that it provides an effective instrument for the description of memory and hereditary properties of various materials and progress. Also, the advantages of the fractional derivatives become apparent in modeling mechanical and electrical properties of real materials, as well as in the description of rheological properties of rocks, and in many other fields.…”

A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids

“…After the KdV model and BO model, a more general evolution model for solitary waves in a finitedepth fluid was given by Kubota, and the model was called intermediate long-wave (ILW) model [12,13]. Many mathematicians solved the above models by all kinds of method and got a series of results [14][15][16][17][18][19]. We note that most of the previous researches about solitary waves were carried out in the zonal area and could not be applied directly to the spherical earth, and little attention had been focused on the solitary waves in the rotational fluids [20].…”