Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed b...Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.展开更多
Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soli...Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.展开更多
Oblique wave interaction with a two-layer breakwater consisting of perforated front and back wall in the presence of bottom undulations is analyzed.Wave characteristics are studied in the framework of small-amplitude ...Oblique wave interaction with a two-layer breakwater consisting of perforated front and back wall in the presence of bottom undulations is analyzed.Wave characteristics are studied in the framework of small-amplitude wave theory,and Darcy’s law is used for flow past porous structures.The varying bottom topography spanned over a finite interval connected by two semi-infinite intervals of uniform water depths.Eigenfunction expansion method is used to handle the solution in the regions of uniform bottom and a modified mild-slope equation along with jump conditions is employed for varying bottom topography.Reflection,transmission,and wave energy dissipation coefficients are obtained numerically by applying the matrix method to understand the effects of several physical quantities such as wavenumber,porosity,and angle of incidence.The transmission coefficient reduces significantly and the wave energy dissipation is high for the present model.Also,Bragg scattering is analyzed in the presence of step-type rippled bottom and presented in this paper.展开更多
We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization ...We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).展开更多
Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time...Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.展开更多
We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the mo...We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kinds of materials.Using probabilistic methods,we present an explicit expression of the fundamental solution under certain conditions.We also derive small-time asymptotic expansion of the PDE’s solutions in the general case.The obtained results are directly usable in applications.展开更多
文摘Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
文摘Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.
基金Saista Tabssum acknowledges the Institute post-doctoral fellowship grant from Indian Institute of Technology,Bombay.
文摘Oblique wave interaction with a two-layer breakwater consisting of perforated front and back wall in the presence of bottom undulations is analyzed.Wave characteristics are studied in the framework of small-amplitude wave theory,and Darcy’s law is used for flow past porous structures.The varying bottom topography spanned over a finite interval connected by two semi-infinite intervals of uniform water depths.Eigenfunction expansion method is used to handle the solution in the regions of uniform bottom and a modified mild-slope equation along with jump conditions is employed for varying bottom topography.Reflection,transmission,and wave energy dissipation coefficients are obtained numerically by applying the matrix method to understand the effects of several physical quantities such as wavenumber,porosity,and angle of incidence.The transmission coefficient reduces significantly and the wave energy dissipation is high for the present model.Also,Bragg scattering is analyzed in the presence of step-type rippled bottom and presented in this paper.
基金supported by National Natural Science Foundation of China(Grant No.11401595)
文摘We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).
基金Supported by the National Natural Science Foundation of China under Grant No.11105057the Foundation of Hubei University of Education under Grant No.2009B013the Project of Excellent Teacher Team of Hubei University of Education under Grant No.2012KB302
文摘Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.
基金supported by the National Science Foundation of USA (Grant No. DMS1206276)National Natural Science Foundation of China (Grant No. 1128101)the Research Unit of Tunisia (Grant No. UR11ES53)
文摘We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kinds of materials.Using probabilistic methods,we present an explicit expression of the fundamental solution under certain conditions.We also derive small-time asymptotic expansion of the PDE’s solutions in the general case.The obtained results are directly usable in applications.
