Evolutionary dynamics of solitary wave profiles and abundant analytical solutions to a(3+1)-dimensional burgers system in ocean physics and hydrodynamics

In the fields of oceanography,hydrodynamics,and marine engineering,many mathematicians and physi-cists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenom-ena,one of which is a(3+1)-dimensional Burgers system that is currently being studied.In this paper,we apply two different analytical methods,namely the generalized Kudryashov(GK)method,and the generalized exponential rational function method,to derive abundant novel analytic exact solitary wave solutions,including multi-wave solitons,multi-wave peakon solitons,kink-wave profiles,stripe solitons,wave-wave interaction profiles,and periodic oscillating wave profiles for a(3+1)-dimensional Burgers sys-tem with the assistance of symbolic computation.By employing the generalized Kudryashov method,we obtain some new families of exact solitary wave solutions for the Burgers system.Further,we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions,exponential rational function solutions,peri-odic breather-wave soliton solutions,dark and bright solitons,singular periodic oscillating wave soliton solutions,and complex multi-wave solutions under various family cases.Based on soft computing via Wolfram Mathematica,all the newly established solutions are verified by back substituting them into the considered Burgers system.Eventually,the dynamical behaviors of some established results are exhibited graphically through three-and two-dimensional wave profiles via numerical simulation.

Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in(3+1)-dimensions with gas bubbles in hydrodynamics and fluids

Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,plasma physics,scientific applications,and marine engineering.The generalized exponen-tial rational function(GERF)technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in(3+1)dimensions,which explains several more nonlinear phenomena in liquids,including gas bubbles.A large number of closed-form wave solutions are generated,including trigonometric function solutions,hyper-bolic trigonometric function solutions,and exponential rational functional solutions.In the dynamics of distinct solitary waves,a variety of soliton solutions are obtained,including single soliton,multi-wave structure soliton,kink-type soliton,combo singular soliton,and singularity-form wave profiles.These de-termined solutions have never previously been published.The dynamical wave structures of some analyt-ical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters.This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics,fluid dynamics,and other fields of nonlinear sciences.

Abundant analytical soliton solutions and different wave profiles to the Kudryashov-Sinelshchikov equation in mathematical physics

The generalized exponential rational function(GERF)method is used in this work to obtain analytic wave solutions to the Kudryashov-Sinelshchikov(K S)equation.The K S equation depicts the occurrence of pressure waves in mixtures of liquid-gas bubbles while accounting for thermal expansion and viscosity.By applying the GERF method to the KS equation,we obtain analytic solutions in terms of trigonometric,hyperbolic,and exponential functions,among others.These solutions include solitary wave solutions,dark-bright soliton solutions,singular soliton solutions,singular bell-shaped solutions,traveling wave solutions,rational form solutions,and periodic wave solutions.We discuss the two-dimensional and three-dimensional graphics of some obtained solutions under the accurate range space by selecting appropriate values for the involved arbitrary parameters to make this research more praiseworthy.The obtained analytic wave solutions specify the GERF method’s dependability,capability,trustworthiness,and efficiency.