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霍赫洛夫-沯波咯慈卡娅方程

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Khokhlov-Zabolotskaya equation
Khokhlov-Zabolotskaya equation

霍赫洛夫-沯波咯慈卡娅方程( Khokhlov--Zabolotskaya equation)是一个非线性偏微分方程[1][2]：

解析解

霍赫洛夫-沯波咯慈卡娅方程有行波解：

p[2] := 1.32+1.4934776966447732662*(1.56+1.7969454312181156991*x^1.2+1.2*C[2]^1.2*y^1.2)^1.2
p[3] := 1.32+1.4934776966447732662*(.2707963267948966192-1.4974545260150964159*x^1.2-1.*C[2]^1.2*y^1.2)^1.2
p[7] := 1.32+1.4934776966447732662((55.009468881881296225-14.965237496723309046*I)*sqrt(1.-.
66321499013806706114*JacobiNS(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2-(.38969456396968710805*I)*JacobiNS(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2)*sqrt(1.-.66321499013806706114*JacobiNS(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2+(.38969456396968710805*I)*JacobiNS(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2)*EllipticF((.84629952125971224961+.23023442302651244686*I)*JacobiNS(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3), .86217948717948717949-.50660293316059324046*I)/sqrt(3000.*JacobiNS(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^4-6725.*JacobiNS(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2+5070.))^1.2
p[8] := 1.32+1.4934776966447732662*(-(34.214441730088728277*I)*sqrt(1.+2.1356058039711429821*JacobiDN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2)*sqrt(1.-2.2476058039711429821*JacobiDN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2)*EllipticF((1.4613712067681992557*I)*JacobiDN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3), 1.0258869993454412308*I)/sqrt(3000.*JacobiDN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^4+70.*JacobiDN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2-625.))^1.2
p[9] := 1.32+1.4934776966447732662*((38.347855408516105018-11.263642905975212858*I)*sqrt(1.-1.3164251207729468599*JacobiCN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2-(.84634523908200302082*I)*JacobiCN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2)*sqrt(1.-1.3164251207729468599*JacobiCN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2+(.84634523908200302082*I)*JacobiCN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2)*EllipticF((1.2003002147146243158+.35255564762321759608*I)*JacobiCN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3), .84115756322748992840-.54079011994043611908*I)/sqrt(5070.*JacobiCN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^4-5450.*JacobiCN(1.68+1.9520491881558575047*x^1.2+1.2*C[2]^1.2*y^1.2, 1.3)^2+2070.))^1.2

p[10] := 1.32+1.4934776966447732662*arctan(1/sqrt(1.2*csc(1.56+1.7969454312181156991*x^1.2+1.2*C[2]^1.2*y^1.2)^2-1.2))^1.2

p[11] := 1.32+1.4934776966447732662*arctan(1/sqrt(1.2*sec(1.56+1.7969454312181156991*x^1.2+1.2*C[2]^1.2*y^1.2)^2-1.2))^1.2
p[12] := 1.32+1.4934776966447732662*arctan(1/sqrt(1.2*sech(1.56+1.7969454312181156991*x^1.2+1.2*C[2]^1.2*y^1.2)^2-1.2))^1.2
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot
Khokhlov-Zabolotskaya equation traveling wave plot

参考文献

  1. ^ Kodama, Y. and Gibbons, J., A method for solving the dispersionless KP hierarchy and its exact solutions, II, Phys. Lett. A,Vol. 135, No. 3, pp. 167–170, 1989.
  2. ^ Anna Rozanova-Pierrat Mathematical analysis of Khokhlov-Zabolotskaya-Kuznetsov (KZK) Equation,2006
  1. *谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社
  2. *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年
  3. 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
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  7. Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
  8. Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
  9. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
  10. Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
  11. Dongming Wang, Elimination Practice,Imperial College Press 2004
  12. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
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