Narrow Results

The fractional Lakshmanan–Porsezian–Daniel equation (LPD) is a significant complex model for the fractional Schrödinger family which arises in quantum physics. This paper explores new bright and kink soliton solutions of the space-time fractional LPD equation with the Kerr law of nonlinearity. By considering the conformable derivatives, the governing model is translated into integer-order differential equations with the aid of an appropriate complex traveling wave transformation. Dynamic behavior and phase portrait of traveling wave solutions are investigated. Further, various types of bright and kinked soliton solutions under definite parametric settings are discussed. Moreover, graphical representations of the obtained solution of the diverse fractional order are depicted to naturally illustrate the constructed solution.

This paper studies optical solitons in 1 + 2 dimensions with power law nonlinearity in the presence of time-dependent coefficients of dispersion, nonlinearity and attenuation. The one-soliton solution to the governing nonlinear Schrödinger equation is obtained and the constraint relation between these coefficients is consequently established. The velocity of the soliton is also obtained in terms of these coefficients. These time-dependent coefficients, which must be Riemann-integrable, are otherwise arbitrary.

This paper carries out the integration of the perturbed nonlinear Schrödinger's equation with log law nonlinearity. The solution is a closed form 1-soliton solution that is obtained by He's semi-inverse variational principle. The soliton amplitude and width are in terms of Lambert's function.