Discretization of Complex Geometric Domain Through Computer-Based Stair-Step Representation Method for Estimating Water Levels Associated with A Storm

In this paper,an improvement has been made to the approximation technique of a complex domain through the stair-step approach to have a considerable accuracy,minimize computational cost,and avoid the hardship of manual work.A novel stair-step representation algorithm is used in this regard,where the entire procedure is carried out through our developed MATLAB routine.Arakawa C-grid is used in our approximation with(1/120)°grid resolution.As a test case,the method is applied to approximate the domain covering the area between 15°-23°N latitudes and 85°-95°E longitudes in the Bay of Bengal.Along with the approximation of the land-sea interface,coastal stations are also identified.Approximated land-sea interfaces and coastal stations are found to be in good agreement with the actual ones based on the similarity index,overlap fraction,and extra fraction criteria.The method can be used for approximating an irregular geometric domain to employ the finite difference method in solving problems related to long waves.As a test case,shallow water equations in Cartesian coordinates are solved on the domain of interest for simulating water levels due to the nonlinear tide-surge interaction associated with the storms April 1991 and AILA,2009 along the coast of Bangladesh.The same input except for the discretized domain and bathymetry as that of Paul et al.(2016)is used in our simulation.The results are found to be in reasonable agreement with the observed data procured from Bangladesh Inland Water Transport Authority.

New exact solutions for the time fractional coupled Boussinesq-Burger equation and approximate long water wave equation in shallow water

The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq-Burger and approximate long water wave equations by using the generalized Kudryashov method.The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann-Liouville derivative sense.Applying the generalized Kudryashov method through with symbolic computer maple package,numerous new exact solutions are successfully obtained.All calculations in this study have been established and verified back with the aid of the Maple package program.The executed method is powerful,effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions with the integer and fractional order.

A variety of novel closed-form soliton solutions to the family of Boussinesq-like equations with different types

This paper deals with the closed-form solutions to the family of Boussinesq-like equations with the effect of spatio-temporal dispersion.The sine-Gordon expansion and the hyperbolic function approaches are efficiently applied to the family of Boussinesq-like equations to explore novel solitary,kink,anti-kink,combo,and singular-periodic wave solutions.The attained solutions are expressed by the trigonometric and hyperbolic functions including tan,sec,cot,csc,tanh,sech,coth,csch,and of their combination.In addition,the mentioned two approaches are applied to the aforesaid models in the sense of Atangana conformable derivative or Beta derivative to attain new wave solutions.Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying the corresponding equations of interest are provided to understand the underlying mechanisms of the stated family.For the bright wave solutions in terms of Atangana’s conformable derivative,the amplitudes of the bright wave gradually decrease,but the smoothness increases when the fractional parametersαandβincrease.On the other hand,the periodicities of periodic waves increase.The attained new wave solutions can motivate applied scientists for engineering their ideas to an optimal level and they can be used for the validation of numerical simulation results in the propagation of waves in shallow water and other nonlinear cases.The performed approaches are found to be simple and efficient enough to estimate the solutions attained in the study and can be used to solve various classes of nonlinear partial differential equations arising in mathematical physics and engineering.

On some novel solution solutions to the generalized Schrödinger-Boussinesq equations for the interaction between complex short wave and real long wave envelope

This paper explores some novel solutions to the generalized Schrödinger-Boussinesq(gSBq)equations,which describe the interaction between complex short wave and real long wave envelope.In order to derive some novel complex hyperbolic and complex trigonometric function solutions,the sine-Gordon equation method(sGEM)is applied to the gSBq equations.Novel complex hyperbolic and trigonometric function solutions are expressed by the dark,bright,combo dark-bright,W-shaped,M-shaped,singular,combo singular,and periodic wave solutions.The accuracy of the explored solitons is examined under the back substitution to the corresponding equations via the symbolic computation software Maple.It is found from the back substitution outcomes that all soliton solutions satisfy the original equations.The proper significance of the explored outcomes is demonstrated by the three-dimensional(3D)and two-dimensional(2D)graphs,which are presented under the selection of particular values of the free parameters.All the combo-soliton(W-shaped,M-shaped,and periodic wave)solutions are found to be new for the interaction between complex short wave and real long wave envelope in laser physics that show the novelty of the study.Moreover,the applied method provides an efficient tool for exploring novel soliton solutions,and it overcomes the complexities of the solitary wave ansatz method.