1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity
Abstract This paper obtains the 1-soliton solution of the Jaulent–Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence.
The first integral method to study the (2+1)-dimensional Jaulent–Miodek equations
In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1)-dimensional Jaulent–Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.
Nuclear spin-lattice relaxation in transition metal compounds with local tetragonal symmetry.
We report on the various contributions to the total spin-lattice relaxation rate in metallic materials with local tetragonal symmetry. The analytical formulae are given in the tight-binding approximation. The calculations show the relation between various partial electron densities of states and corresponding contributions to the relaxation rates. The presented formulae can be used to compare theoretically calculated electron band structure parameters with those obtained from NMR spin-lattice relaxation time measurements.