Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer alg...Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.展开更多
We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial different...We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.展开更多
Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an a...Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions.展开更多
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
Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebrai...Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.展开更多
By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial dif...By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.展开更多
Objective: to observe the therapeutic effect of dexamethasone palmitate injection on hoarseness caused by recurrent laryngeal nerve injury during thyroid surgery. Methods: 783 patients were divided into treatment grou...Objective: to observe the therapeutic effect of dexamethasone palmitate injection on hoarseness caused by recurrent laryngeal nerve injury during thyroid surgery. Methods: 783 patients were divided into treatment group (395 cases) and control group (388 cases). After thyroidectomy, the treatment group was sprayed with dexamethasone palmitate injection 1ml:4mg, while the control group was not sprayed with any drugs. The patients' hoarseness was observed on the 1st, 3rd, 7th and 30th day after operation. The GRBAS score, voice disorder index and VHI-13 Chinese version scale were used to evaluate the patients' voice. At the same time, the occurrence of severe adverse drug reactions, upper abdominal pain and hyperglycemia within 7 days after operation, and the infection in the operation area within 30 days after operation were observed. Results: the hoarseness in the treatment group was less than that in the control group on the 1st, 3rd and 7th day after operation (p<0.05), and there was no significant difference between the two groups on the 30th day after operation (p>0.05). There was no serious adverse drug reaction in the treatment group, upper abdominal pain and hyperglycemia within 7 days after operation, and there was no significant difference between the two groups within 30 days after operation (p>0.05). Conclusion: local application of dexamethasone palmitate injection during thyroid surgery has a certain therapeutic effect on reducing hoarseness caused by recurrent laryngeal nerve injury, but it has a limited therapeutic effect on recurrent laryngeal nerve injury which has not recovered its voice 30 days after operation.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10072013the National Key Basic Research Development Program under Grant No.G1998030600
文摘Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.
文摘We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.
文摘Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions.
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.
基金The project supported by National Natural Science Foundation of China under Grant No.10072013the State Key Basic Research Development Program under Grant No.G1998030600
文摘Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.
文摘By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.
文摘Objective: to observe the therapeutic effect of dexamethasone palmitate injection on hoarseness caused by recurrent laryngeal nerve injury during thyroid surgery. Methods: 783 patients were divided into treatment group (395 cases) and control group (388 cases). After thyroidectomy, the treatment group was sprayed with dexamethasone palmitate injection 1ml:4mg, while the control group was not sprayed with any drugs. The patients' hoarseness was observed on the 1st, 3rd, 7th and 30th day after operation. The GRBAS score, voice disorder index and VHI-13 Chinese version scale were used to evaluate the patients' voice. At the same time, the occurrence of severe adverse drug reactions, upper abdominal pain and hyperglycemia within 7 days after operation, and the infection in the operation area within 30 days after operation were observed. Results: the hoarseness in the treatment group was less than that in the control group on the 1st, 3rd and 7th day after operation (p<0.05), and there was no significant difference between the two groups on the 30th day after operation (p>0.05). There was no serious adverse drug reaction in the treatment group, upper abdominal pain and hyperglycemia within 7 days after operation, and there was no significant difference between the two groups within 30 days after operation (p>0.05). Conclusion: local application of dexamethasone palmitate injection during thyroid surgery has a certain therapeutic effect on reducing hoarseness caused by recurrent laryngeal nerve injury, but it has a limited therapeutic effect on recurrent laryngeal nerve injury which has not recovered its voice 30 days after operation.
