New exact soliton solutions, bifurcation and multistability behaviors of traveling waves for the (3+1)-dimensional modified Zakharov-Kuznetsov equation with higher order dispersion

The goal of the present paper is to obtain and analyze new exact travelling wave solutions and bifurcation behavior of modified Zakharov-Kuznetsov (mZK) equation with higher order dispersion term. For this purpose, first and second simple methods are used to build soliton solutions of travelling wave solutions. Furthermore, bifurcation behavior of traveling waves including new type of quasiperiodic and multi-periodic traveling wave motions have been examined depending on the physical parameters. Multistability for the nonlinear mZK equation has been investigated depending on fixed values of physical parameters with various initial conditions. The suggested methods for the analytical solutions are powerful and benefical tools to obtain the exact travelling wave solutions of nonlinear evolution equations (NLEEs). Two and three-dimensional plots are also provided to illustrate the new solutions. Bifurcation and multistability behaviors of traveling wave solution of the nonlinear mZK equation with higher order dispersion will add some value in the literature of mathematical and plasma physics.

Enhanced Pulse Compression within Sign-Alternating Dispersion Waveguides

We show theoretically and numerically how to optimize sign-alternating dispersion waveguides for maximum nonlinear pulse compression, while leveraging the substantial increase in bandwidth-to-input peak power advantage of these structures. We find that the spectral phase can converge to a parabolic profile independent of uncompensated higher-order dispersion. The combination of an easy to compress phase spectrum, with low input power requirements, then makes sign-alternating dispersion a scheme for high-quality nonlinear pulse compression that does not require high powered lasers, which is beneficial for instance in integrated photonic circuits. We also show a new nonlinear compression regime and soliton shaping dynamic only seen in sign-alternating dispersion waveguides. Through an example SiN-based integrated waveguide, we show that the dynamic enables the attainment of compression to two optical cycles at a pulse energy of 100 pJ which surpasses the compression achieved using similar parameters for a current state-of-the-art SiN system.

Fractal Higher-order Dispersions Model and Its Fractal Variational Principle Arising in the Field of Physcial Process

This paper introduces the fractal version of the higher-order dispersion model for the construction of novel soliton solutions through fractal variational technology. Higher-order dispersion model theoretical study of the soliton propagation dynamics is known in the absence of self-phase modulation. In the context of negligibly small group velocity dispersion, this model involves higher-order spatio-temporal dispersion and can be a core component of the telecommunications industry. Using the variational approach, the model effectively produces bright and dark soliton solutions. Essential novel conditions guaranteeing the existence of suitable solitons have been developed. The 3D, 2D and contour graphs of the computed effects are seen in the collection of the relevant parameter values. This study shows the significance and immense latency of variational technologies to the derivative nonlinear Schrödinger equation (DNLSE).

Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.