Using the generalized conditional symmetry approach, a complete list of canonical forms for the Korteweg de-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is ob...Using the generalized conditional symmetry approach, a complete list of canonical forms for the Korteweg de-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained. The exact DDFSSs of the resulting equations are explicitly exhibited.展开更多
A general type of local/zed excitations, folded solitary waves and foldons, is defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicat...A general type of local/zed excitations, folded solitary waves and foldons, is defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess qnite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the real natural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universal formul is valid for some quite universal (2+1)-dimensional physical mode/s. The "universal" formula is also extended to a more general form with many more independent arbitrary functions.展开更多
Using the generalized conditional symmetry approach, we obtain a number of new generalized (1+1)-dimensional nonlinear wave equations that admit derivative-dependent functional separable solutions.
We numerically simulate the processing of the phase separation of the polymer blend-particle system under fluctuating fields by new discretization's form. Due to the presence of oscillatory particles which have an...We numerically simulate the processing of the phase separation of the polymer blend-particle system under fluctuating fields by new discretization's form. Due to the presence of oscillatory particles which have an affinity for one of the components, the ordering mechanism of phase separation will be changed. By changing the oscillatory frequency ω and amplitude γ, we can find the formation of the striped structures either parallel or perpendicular to the oscillatory direction and obtain a diagram describing the orientational ordering of the domain structures.展开更多
The special soliton solutions of Bogoyavlenskii coupled KdV equations are obtained by means of the standard Weiss-Tabor-Carnvale Painleve truncation expansion and the nonstandard truncation of a modified Conte's i...The special soliton solutions of Bogoyavlenskii coupled KdV equations are obtained by means of the standard Weiss-Tabor-Carnvale Painleve truncation expansion and the nonstandard truncation of a modified Conte's invariant Painleve expansion.展开更多
In the framework of the functional integral formalism, we calculate the effective potential of the double sine-Gordon (DsG) model up to the second order with an optimized expansion and the Coleman's normal-orderin...In the framework of the functional integral formalism, we calculate the effective potential of the double sine-Gordon (DsG) model up to the second order with an optimized expansion and the Coleman's normal-ordering prescription. Within the range of convergence, we make a comparison among the classicaland the effective potential of the first and second order. The numerical analysis shows that the DsG post-Gaussian EP possesses some fine global properties and makes a substantial and a concordant quantum correction to the features of the classical potential.展开更多
The Adomian decomposition method is used to solve the Cauchy problem of the perturbed KdV equation.Three types of exact solitary wave solutions are reobtained via the A domian's approach by selecting the initial c...The Adomian decomposition method is used to solve the Cauchy problem of the perturbed KdV equation.Three types of exact solitary wave solutions are reobtained via the A domian's approach by selecting the initial conditionsappropriately.展开更多
By means of a simple ideal, which is firstly proposed for the continuous system, we present an arbitrary order classical Toda family invariant under common Virasoro-type symmetry algebra.
文摘Using the generalized conditional symmetry approach, a complete list of canonical forms for the Korteweg de-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained. The exact DDFSSs of the resulting equations are explicitly exhibited.
文摘A general type of local/zed excitations, folded solitary waves and foldons, is defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess qnite rich structures and abundant interaction properties. The folded phenomenon is quite universal in the real natural world. The folded solitary waves and foldons are obtained from a quite universal formula and the universal formul is valid for some quite universal (2+1)-dimensional physical mode/s. The "universal" formula is also extended to a more general form with many more independent arbitrary functions.
基金The project supported by the National Outstanding Youth Foundation of China (No.19925522)+2 种基金the Research Fund for the Doctoral Program of Higher Education of China (Grant.No.2000024832)National Natural Science Foundation of China (No.90203001)
文摘Using the generalized conditional symmetry approach, we obtain a number of new generalized (1+1)-dimensional nonlinear wave equations that admit derivative-dependent functional separable solutions.
文摘We numerically simulate the processing of the phase separation of the polymer blend-particle system under fluctuating fields by new discretization's form. Due to the presence of oscillatory particles which have an affinity for one of the components, the ordering mechanism of phase separation will be changed. By changing the oscillatory frequency ω and amplitude γ, we can find the formation of the striped structures either parallel or perpendicular to the oscillatory direction and obtain a diagram describing the orientational ordering of the domain structures.
文摘The special soliton solutions of Bogoyavlenskii coupled KdV equations are obtained by means of the standard Weiss-Tabor-Carnvale Painleve truncation expansion and the nonstandard truncation of a modified Conte's invariant Painleve expansion.
文摘In the framework of the functional integral formalism, we calculate the effective potential of the double sine-Gordon (DsG) model up to the second order with an optimized expansion and the Coleman's normal-ordering prescription. Within the range of convergence, we make a comparison among the classicaland the effective potential of the first and second order. The numerical analysis shows that the DsG post-Gaussian EP possesses some fine global properties and makes a substantial and a concordant quantum correction to the features of the classical potential.
文摘The Adomian decomposition method is used to solve the Cauchy problem of the perturbed KdV equation.Three types of exact solitary wave solutions are reobtained via the A domian's approach by selecting the initial conditionsappropriately.
文摘By means of a simple ideal, which is firstly proposed for the continuous system, we present an arbitrary order classical Toda family invariant under common Virasoro-type symmetry algebra.
