First,we studied the invariance properties of the Kadomstev–Petviashvili equation with power law nonlinearity.Then,we determined the complete class of conservation laws and stated the corresponding conserved densitie...First,we studied the invariance properties of the Kadomstev–Petviashvili equation with power law nonlinearity.Then,we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation.The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows.展开更多
In this paper,a novel method,named the consistent Burgers equation expansion(CBEE)method,is proposed to solve nonlinear evolution equations(NLEEs)by the celebrated Burgers equation.NLEEs are said to be CBEE solvable i...In this paper,a novel method,named the consistent Burgers equation expansion(CBEE)method,is proposed to solve nonlinear evolution equations(NLEEs)by the celebrated Burgers equation.NLEEs are said to be CBEE solvable if they are satisfied by the CBEE method.In order to verify the effectiveness of the CBEE method,we take(2+1)-dimensional Burgers equation as an example.From the(1+1)-dimensional Burgers equation,many new explicit solutions of the(2+1)-dimensional Burgers equation are derived.The obtained results illustrate that this method can be effectively extended to other NLEEs.展开更多
文摘First,we studied the invariance properties of the Kadomstev–Petviashvili equation with power law nonlinearity.Then,we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation.The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows.
基金supported by Natural Science Foundation of Hebei Province,China(No.A2018207030)Youth Key Program of Hebei University of Economics and Business(2018QZ07)+2 种基金Key Program of Hebei University of Economics and Business(2020ZD11)Youth Team Support Program of Hebei University of Economics and Business,Study on system dynamics of scientific and technological innovation promoting the expansion and quality of residents’consumption in Hebei Province(20556201D)Youth Top-notch Talent Support Program of Higher Education of Hebei Province of China(BJ2020011)。
文摘In this paper,a novel method,named the consistent Burgers equation expansion(CBEE)method,is proposed to solve nonlinear evolution equations(NLEEs)by the celebrated Burgers equation.NLEEs are said to be CBEE solvable if they are satisfied by the CBEE method.In order to verify the effectiveness of the CBEE method,we take(2+1)-dimensional Burgers equation as an example.From the(1+1)-dimensional Burgers equation,many new explicit solutions of the(2+1)-dimensional Burgers equation are derived.The obtained results illustrate that this method can be effectively extended to other NLEEs.
