Homotopic Mapping Method Research Articles

The homotopic mapping solutions for the generalized Schrödinger equation

This work is concerned on how to find the approximation solutions of the generalized Schrödinger equation by using the homotopic mapping method. First, we give the basic idea of Homotopic mapping method. In the following, we introduce a homotopic mapping, and make the generalized Schrödinger equation do a homotopic deformation, then we get the approximation solutions in given initial conditions. Finally we give two examples about derivative Schrödinger equation and Hirota equation to illustrate efficiency of this method, and the exact solutions of these equations can be solved in the condition of selecting proper auxiliary function v.

Homotopic Approximate Solutions for the Perturbed CKdV Equation with Variable Coefficients

This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation εu n are also induced.

Homotopic mapping solving method of transfers model with a class of generalized femtosecond pulse laser for nano metal

A class of transfer model for femtosecond pulse laser nano metal film is investigated. Firstly, the exact solution of a typical model is obtained. And then, the arbitrary order approximate analytic solution of corresponding model is obtained by using the functional homotopic mapping method. Finally, the meaning of solution is discussed.

Soliton solution for the disturbed mKdV coupled system

The approximate solution for a class of disturbed mKdV coupled system is considered using a simple and valid technique. We first solve the approximate solution of the soliton for a corresponding complex-valued differential equation using the homotopic mapping method. And then the approximate solution of the soliton for a original disturbed mKdV coupled system is obtained.

Approximate solution for a class of relative rotation nonlinear dynamic model

A class of relative rotation nonlinear dynamical model with nonlinear damping force and forcing periodic force is investigated. First, a homotopic mapping is constructed, and then the initial approximate solution is determined. Finally, using the homotopic mapping method, the arbitrarily degree approximation for corresponding model is found.

The solutions for disturbed El Ni o/La Ni a-southern oscillation model

The EI Ni o/La Ni a and the Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. This paper, aims at creating an approximate solving method of nonlinear equation for the ENSO models. And based on a class of oscillator of ENSO models, employing the method of homotopic mapping, the approximate and exact solutions of the corresponding problem is studied. The accuracy of approximate solution is discussed. It is proved from the results that homotopic method can be used for analyzing the SST anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.

Soliton solution to generalized nonlinear disturbed Klein-Gordon equation

A generalized nonlinear disturbed Klein-Gordon equation is studied. Using the homotopic mapping method, the corresponding homotopic mapping is constructed. A suitable initial approximation is selected, and an arbitrary-order approximate solution to the soliton is calculated. A weakly disturbed equation is also studied.

Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation

A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original generalized complex Burgers equation is obtained. This method can find the approximation of arbitrary order of precision simply and reliably.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopic mapping method.

Homotopic mapping solution of soliton for a class of disturbed Burgers equation

The problem of solving a class of disturbed Burgers equation is considered. Using the homotopic mapping method and theory ,the approximate solution with arbitrary degree of accuracy for the solitary wave is obtained.

Approximate solution of sea-air oscillator for El Ni?o-southern oscillation model

A class of time delayed coupled system of the El Ni&#241,o-southern oscillation (ENSO) model is considered. By using the homotopic mapping method, the approximate expansion of the solution for the ENSO model is obtained and the asymptotic behavior of solution of corresponding problem is studied.

Approximate analytic solution of solitary wave for a class of nonlinear disturbed Nizhnik-Novikov-Veselov system

摘要 采用了一个简单而有效的技巧，研究了一类非线性扰动Nizhnik-Novikov-Veselov系统. 首先引入一个相应典型系统的孤立波解. 然后利用同伦映射方法得到了原非线性扰动Nizhnik-Novikov-Veselov系统的近似解析解. 关键词: 孤立波 / 扰动Nizhnik-Novikov-Veselov系统 / 同伦映射 Abstract The approximate analytic solution for a class of nonlinear disturbed Nizhnik-Novikov-Veselov system is considered by a simple and valid technique. We first introduce the approximate solution of a corresponding typical differential system. And then the approximate analytic solution for the original nonlinear disturbed Nizhnik-Novikov-Veselov system is obtained using the homotopic mapping method. Keywords: solitary wave / disturbed Nizhnik-Novikov-Veselov systrm / homotopic mapping 作者及机构信息 莫嘉琪1, 陈贤峰2 (1)安徽师范大学数学系，芜湖 241000；上海高校计算科学E-研究院SJTU研究所，上海 200240; (2)上海交通大学数学系，上海 200240；上海高校计算科学E-研究院SJTU研究所，上海 200240 基金项目: 国家自然科学基金(批准号：40676016，40876010),中国科学院知识创新工程重要方向项目(批准号：KZCX2-YW-Q03-08) ,LASG国家重点实验室专项经费和上海市教育委员会E-研究院建设计划(批准号：E03004)，公益行业（气象）科研专项（批准号：GYHY200806010）和浙江省自然科学基金（批准号：6090164）资助的课题. Authors and contacts Mo Jia-Qi1, Chen Xian-Feng2 (1)安徽师范大学数学系，芜湖 241000；上海高校计算科学E-研究院SJTU研究所，上海 200240; (2)上海交通大学数学系，上海 200240；上海高校计算科学E-研究院SJTU研究所，上海 200240 参考文献 [1] ［1］McPhaden M J, Zhang D 2002 Nature 415 603 [2] ［2］Gu D F, Philander S G H 1997 Science 275 805 [3] ［3］Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) ［马松华、 强继业、 方建平 2007 物理学报 56 620］ [4] ［4］Ma S H, Qiang J Y, Fang J P 2007 Comm. Theor. Phys. 48 662 [5] ［5］Loutsenko I 2006 Comm. Math. Phys. 268 465 [6] ［6］Gedalin M 1998 Phys. Plasmas 5 127 [7] ［7］Parkes E J 2008 Chaos Solitons Fractals 38 154 [8] ［8］Pan L S, Zou W M 2005 Acta Phys. Sin. 54 1 (in Chinese)［潘留仙、 左伟明 2005 物理学报 54 1］ [9] ［9］Pan L S, Liu J L, Li S S, Niu Z C, Feng S L, Zheng H Z 2002 Science in China A 32 556 (in Chinese) ［潘留仙、 刘金龙、 李树深、 牛智川、 封松林、 郑厚值 2002 中国科学 A 32 556］ [10] ］Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese) ［封国林、戴新刚、 王爱慧、 丑纪范 2001 物理学报50 606］ [11] ］Wang L S, Xu D Y 2003 Science in China E 32 488 (in Chinese) ［王林山、 徐道义 2003 中国科学E 32 488］ [12] ］Wang M L 1995 Phys. Lett. A 199 169 [13] ］Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese) ［吴国将、韩家骅、史良马、张苗 2006 物理学报 55 3858］ [14] ］Li X Z, Li X Y, Zhang L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese) ［李向正、李修勇、 赵丽英、 张金良 2008 物理学报 57 2203］ [15] ］Li Z H, Zhang S Q 1997 Acta Math. Phys. Sin. 17 81 (in Chinese) ［李志斌、 张善卿 1997 数学物理学报 17 81］ [16] ］Gao L, Xu W, Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860 (in Chinese) ［高亮、 徐伟、唐亚宁、 申建伟 2007 物理学报 56 1860］ [17] ］Ma S H, Wu X H, Fang J P, Zhang X L 2008 Acta Phys. Sin. 57 11 (in Chinese) ［马松华、 吴小红、 方建平、 郑春龙 2008 物理学报 57 11］ [18] ］Bekir A 2008 Phys. Lett. A 372 2254 [19] ］Li B Q, Ma Y L 2009 Acta Phys. Sin. 58 4373 (in Chinese) ［李帮庆、 马玉兰 2009 物理学报 58 4373］ [20] ］Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York，CRC Press Co) [21] ］He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Shengzhou: Henan Science and Technology Press) (in Chinese) ［何吉欢 2002 工程和科学计算中的近似非线性分析方法 (郑州 河南科学技术出版社)］ [22] ］Graef J R, Kong L 2008 Math. Proc.Camb. Philos. Soc. 145 489 [23] ］Hovhannisyan G, Vulanovic R 2008 Nonlinear Stud. 15 297 [24] ］Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392 [25] ］Ramos M, 2009 J. Math. Anal. Appl. 352 246 [26] ］Mo J Q, Zhu J, Wang H 2003 Prog. Nat. Sci. 13 768 [27] ］Mo J Q 2009 Chin. Phys. Lett. 26 060202-1 [28] ］Mo J Q, Cheng Yan 2009 Acta Phys. Sin. 58 4379 (in Chinese) ［莫嘉琪、程燕 2009 物理学报 58 4379］ [29] ］Mo J Q 2009 Science in China， G 52 1007 [30] ］Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) ［莫嘉琪、 林万涛、 林一骅 2007物理学报 56 3127］ [31] ］Mo J Q, Lin W T 2008 Acta Phys. Sin. 57 6689 (in Chinese) ［莫嘉琪、 林万涛 2008物理学报 57 6689］ 施引文献

Approximation solution of a class of disturbed sea-air coupled oscillator mechanism

A box model of the interhemispheric thermohaline circulation in the disturbed sea-air for globe climate is considered. By using the homotopic mapping method，a class of nonlinear model is studied, and the approximate solution is obtained. The homotopic mapping solving method is an analytic method，the solution obtained can be analytically operated sequentially. And then we can also study the diversified qualitative and quantitative behaviors of corresponding physical quantities.

Approximate solution of solitary wave for a class of generalized nonlinear disturbed dispersive equation

The approximate solution for a class of nonlinear disturbed dispersive equation is considered using a simple and valid technique. We first introduce the solitary wave solution of the corresponding typical differential equation, and then the approximate solution of the singular solitary wave for an original nonlinear disturbed dispersive equation is obtained using the homotopic mapping method.

Solitary wave series solution for generalized (3+1)-dimensional nonlinear Burgers system

A class of generalized (3+1)-dimensional nonlinear Burgers system is studied. Using the homotopic mapping method, the corresponding mapping expansions are constructed and using the iteration method the series solution of travelling wave for a solitary wave is obtained.

Approximation of the soliton solution for the generalized Vakhnenko equation

A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemko equation is obtained. By this method an arbitrary order approximation can be easily obtained and, similarly, approximate soliton solutions of other nonlinear equations can be acquired.

Homotopic mapping solution of an oscillator for the El Niño/La Niña-southern oscillation

This paper considers a class of oscillator for the El Niño/La Niña-southern oscillation (ENSO) model. By using the homotopic mapping method, it obtains approximations of the solution for the ENSO model.

The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation

This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method, it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping, it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method, it possesses a good accuracy.

Homotopic mapping solving method for gain fluency of a laser pulse amplifier

The model for gain fluency of a laser pulse amplifier is studied. Using the homotopic mapping method, firstly, the system of the original model is packed up standardization; secondly, introducing a homotopic mapping, taking the property of the mapping, inducing a contrived parameter, the solving of a nonlinear problem translates into the solving of a linear problem. Then the approximate expressions of the solution for the corresponding model are obtained. And the precision for the approximate solution is compared. It illuminates that the obtained approximate solution using the homotopic mapping method possesses higher approximate degree. At one time, the expansion of solution through the homotopic mapping method can be kept in the analytic operation. Thus it also enables us through differential and integral operations to obtain other physics behavior for the gain fluency of laser pulse amplifier.

A class of homotopic solving method for ENSO model

The El Niño/La Niña and the Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this article, the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models. And on the basis of a class of oscillator of ENSO models, using the method of homotopic mapping, the approximation of solution of corresponding problem is studied. It is proved from the results that homotopic method can be used for analyzing the SST anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.