Exact solutions of the (3+1)-generalized fractional nonlinear wave equation with gas bubbles.

In this manuscript, we implement the travelling wave solutions of the fractional (3+1) generalized computational nonlinear wave equation with gas bubbles via application of five mathematical methods. Liquids with gas bubbles primarily arise in various applications like science, engineering, and mathematical physics. The obtained solitary waves solutions have fruitful applications in engineering, science, life, nature and physics. Several novel soliton solutions of concerned model are established in the form of hyperbolic, trigonometric, exponential and rational functions. To handle all calculations and verification of obtained results, computational software Mathematica 12.1 is used. For the demonstration of the physical behaviour of concern model, some solutions are plotted graphical in 2-dimensional and 3-dimensional by imparting specific values to the parameters under constrain conditions. Finally, we intrigue both two and three dimensional to explain the physical behavior of the model.

New soliton molecules to couple of nonlinear models: ion sound and Langmuir waves systems.

In this paper, we will study two various nonlinear models: the Atangana-Baleanu fractional system of equations for the ion sound and Langmuir waves (ISALWs) and Hirota Ramani equation to obtain variety of solitary wave solutions. We will obtain bright, dark, periodic wave and solitory wave for ISALWs equation. We will also retreived bell type, kink type, singular, Jacbion elliptic function, Weierstrass-elliptic function, hyperbolic functions, periodic functions and other solitary wave solutions for Hirota Ramani equation using Sub ODE technique under some constraint conditions. At the end we will present our solutions with the help of graphs in distinct dimensions.

Multiple lump and interaction solutions for fifth-order variable coefficient nonlinear-Schrödinger dynamical equation.

Lump and their interactions with kink, periodic and rogue waves, and periodic cross lump waves will be studied for fifth-order variable coefficient nonlinear-Schrödinger equation in this paper. With the combinations of bilinear, exponent, and trigonometric functions, we'll study different lump soliton solutions. With interaction phenomenon we'll set up some new analytical solutions and also represents them in graphical ways.

Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity.

This article retrieve lump, lump with one kink and rogue wave soliton for the time fractional resonant nonlinear Schrödinger equation with parabolic law having weak nonlocal nonlinearity. According to theory of dynamical systems, Schrödinger equation may be converted into plane systems. We use Hirota bilinear method to obtained these solutions. At the end, we present graphical representation of our results in various dimensions.

Study of global dynamics of COVID-19 via a new mathematical model.

The theme of this paper focuses on the mathematical modeling and transmission mechanism of the new Coronavirus shortly noted as (COVID-19), endangering the lives of people and causing a great menace to the world recently. We used a new type epidemic model composed on four compartments that is susceptible, exposed, infected and recovered (SEIR), which describes the dynamics of COVID-19 under convex incidence rate. We simulate the results by using nonstandard finite difference method (NSFDS) which is a powerful numerical tool. We describe the new model on some random data and then by the available data of a particular regions of Subcontinents.