Comptes Rendus
no. 11-12
Partial Differential Equations
Meromorphic solutions of generalized inviscid Burgers’ equations and related PDES
Feng Lü1
1 College of Science, China University of Petroleum, Qingdao Shandong, 266580, P.R. China
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1169-1178.

The purposes of this paper are twofold. The first one is to describe entire solutions of certain type of PDEs in ℂ n with the modified KdV-Burgers equation and modified Zakharov-Kuznetsov equation as the prototypes. The second one is to characterize entire and meromorphic solutions of generalized inviscid Burgers’ equations in ℂ 2 .

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.136
Classification: 35F20, 32A15, 32A22

Feng Lü 1

1 College of Science, China University of Petroleum, Qingdao Shandong, 266580, P.R. China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{CRMATH_2020__358_11-12_1169_0,
     author = {Feng L\"u},
     title = {Meromorphic solutions of generalized inviscid {Burgers{\textquoteright}} equations and related {PDES}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1169--1178},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.136},
     language = {en},
}
TY  - JOUR
AU  - Feng Lü
TI  - Meromorphic solutions of generalized inviscid Burgers’ equations and related PDES
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 1169
EP  - 1178
VL  - 358
IS  - 11-12
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.136
LA  - en
ID  - CRMATH_2020__358_11-12_1169_0
ER  - 
%0 Journal Article
%A Feng Lü
%T Meromorphic solutions of generalized inviscid Burgers’ equations and related PDES
%J Comptes Rendus. Mathématique
%D 2020
%P 1169-1178
%V 358
%N 11-12
%I Académie des sciences, Paris
%R 10.5802/crmath.136
%G en
%F CRMATH_2020__358_11-12_1169_0
Feng Lü. Meromorphic solutions of generalized inviscid Burgers’ equations and related PDES. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1169-1178. doi : 10.5802/crmath.136. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.136/

[1] Der-Chen Chang; Bao Qin Li; Chung-Chun Yang On composition of meromorphic functions in several complex variables, Forum Math., Volume 7 (1995), pp. 77-94 | MR | Zbl

[2] Peter V. Dovbush Normal functions of many complex variables, Mosc. Univ. Math. Bull., Volume 36 (1981) no. 1, pp. 44-48 | Zbl

[3] Peter V. Dovbush Zalcman’s lemma in ℂ n , Complex Var. Theory Appl., Volume 65 (2020) no. 5, pp. 796-800 | DOI | MR | Zbl

[4] R. D. Fay Plane sound waves of finite amplitude, J. Acoust. Soc. Am., Volume 3 (1931), pp. 222-241 | DOI | Zbl

[5] M. M. M. Hassan New exact solutions of two nonlinear physical models, Commun. Theor. Phys., Volume 53 (2010) no. 4, pp. 596-604 | DOI | MR | Zbl

[6] Walter Kurt Hayman Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, 1964 | Zbl

[7] Pei-Chu Hu; Bao Qin Li On meromorphic solutions of linear partial differential equations of second order, J. Math Anal Appl., Volume 393 (2012) no. 1, pp. 200-211 | MR | Zbl

[8] Pei-Chu Hu; Chung-Chun Yang Malmquist type theorem and factorization of meromorphic solutions of partial differential equations, Complex Var. Theory Appl., Volume 27 (1995) no. 3, pp. 269-285 | MR | Zbl

[9] Pei-Chu Hu; Chung-Chun Yang Unicity of Meromorphic Mappings, Advances in Complex Analysis and its Applications, 1, Kluwer Academic Publishers, 2003 | MR | Zbl

[10] Pei-Chu Hu; Chung-Chun Yang Global solutions of homogeneous linear partial differential equations of the second order, Mich. Math. J., Volume 58 (2009) no. 3, pp. 807-831 | MR | Zbl

[11] Pei-Chu Hu; Chung-Chun Yang The Tumura–Clunie theorem in several complex variables, Bull. Aust. Math. Soc., Volume 90 (2014) no. 3, pp. 444-456 | MR | Zbl

[12] Pei-Chu Hu; Chung-Chun Yang On complex solutions of certain partial differential equations, Complex Var. Elliptic Equ., Volume 62 (2017) no. 10, pp. 1492-1505 | MR | Zbl

[13] Robert O. Kujala Functions of finite λ-type in several complex variables, Trans. Am. Math. Soc., Volume 161 (1971), pp. 327-358 | MR | Zbl

[14] Bao Qin Li On reduction of functional-differential equations, Complex Var. Theory Appl., Volume 31 (1996) no. 4, pp. 311-324 | MR | Zbl

[15] Bao Qin Li Entire solutions of certain partial differential equations and factorization of partial derivatives, Trans. Am. Math. Soc., Volume 357 (2005) no. 8, pp. 3169-3177 | MR | Zbl

[16] Bao Qin Li entire solutions of u z 1 m +u z 2 n =e g , Nagoya Math. J., Volume 178 (2005), pp. 151-162 | Zbl

[17] Bao Qin Li On meromorphic solutions of f 2 +g 2 =1, Math. Z., Volume 258 (2008) no. 4, pp. 763-771 | Zbl

[18] Liangwen Liao; Weiyi Su; Chung-Chun Yang A Malmquist–Yosida type of theorem for the second-order algebraic differential equations, J. Differ. Equ., Volume 187 (2003) no. 1, pp. 63-71 | DOI | MR | Zbl

[19] Feng Lü; Junfeng Xu; Ang Chen Entire functions sharing polynomials with their first derivatives, Arch. Math., Volume 92 (2009) no. 6, pp. 593-601 | MR | Zbl

[20] Ervin Y. Rodin A Riccati solution for Burgers’ equation, Q. Appl. Math., Volume 27 (1970), pp. 541-545 | DOI | MR | Zbl

[21] Elias George Saleeby Meromorphic solutions of generalized inviscid Burgers’ equations and a family of quadratic PDEs, J. Math. Anal. Appl., Volume 425 (2015) no. 1, pp. 508-519 | DOI | MR | Zbl

[22] Wilhelm Stoll Introduction to Value Distribution Theory of Meromorphic Maps, Lecture Notes in Mathematics, 950, Springer, 1982 | MR | Zbl

[23] Richard M. Timoney Bloch functions in several complex variables I, Bull London Math Soc., Volume 12 (1980) no. 4, pp. 241-267 | DOI | MR | Zbl

[24] EROL Varoglu; W. D. Liam Finn Space-time finite elements incorporating characteristics for the Burgers’ equation, Int. J. Numer. Meth. Engng., Volume 16 (1980) no. Special Issue, p. 1716-184 | MR | Zbl

[25] Al Vitter The lemma of the logarithmic derivative in seveal complex variables, Duke Math. J., Volume 44 (1977) no. 1, pp. 89-104 | DOI | MR | Zbl

[26] Wenjun Yuan; Yong Huang; Yadong Shang All traveling wave exact solutions of two nonlinear physical models, Appl. Math. Comput., Volume 219 (2013) no. 11, pp. 6212-6223 | MR | Zbl

[27] Lawrence Zalcman Normal families: new perspectives, Bull. Am. Math. Soc., Volume 35 (1998) no. 3, pp. 215-230 | DOI | MR | Zbl

Cited by Sources:

Comments - Policy