林家翘-钱学森方程

利用Maple中的软件包TWS_solution可得林-钱方程的多种行波解^[3]

${\displaystyle u(x,y,t)=TWS_{s}ol:={u(x,y,t)=_{C}1+(-(1/2)*ln(tanh(_{C}3+_{C}4*x+_{C}5*y+_{C}6*t)+1)+(1/2)*ln(tanh(_{C}3+_{C}4*x+_{C}5*y+_{C}6*t)-1))*_{C}2}}$ 

${\displaystyle g[2]:={u(x,y,t)=_{C}1+arctan(1/{\sqrt {(}}csc(_{C}3+_{C}4*x+_{C}5*y+_{C}6*t)^{2}-1))*_{C}2}}$ 

${\displaystyle g[2]:={u(x,y,t)=_{C}1+(-(1/2)*ln(coth(_{C}3+_{C}4*x+_{C}5*y+_{C}6*t)+1)+(1/2)*ln(coth(_{C}3+_{C}4*x+_{C}5*y+_{C}6*t)-1))*_{C}2}}$ 

${\displaystyle g[2]:={u(x,y,t)=_{C}1+arctanh(1/{\sqrt {(}}1+csch(_{C}3+_{C}4*x+_{C}5*y+_{C}6*t)^{2}))*_{C}2}}$ 

找到了一个新的可积（3 + 1）维泛化; 看系统（40）在纸 ^[4]

1. ^ William F. Ames. Nonlinear partial differential equations in engineering, Vol. 18 （页面存档备份，存于互联网档案馆）. Academic Press, p. 173, 1965.
2. ^ C.C. Lin, E.Reissner,and H.S.Tsien, On Two Dimensional Non-steady Motion of a Slender Body in a Compressible Fluid, 钱学森文集 p513 上海交通大学出版社
3. ^ Graham W. Griffiths Willian Schiesser, Traveling wave analysis of Partial Differential Equations p436
4. ^ A. Sergyeyev, New integrable (3+1)-dimensional systems and contact geometry, Lett. Math. Phys. 108 (2018), no. 2, 359-376, https://arxiv.org/abs/1401.2122 （页面存档备份，存于互联网档案馆）

• D. Zwillinger. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 138, 1997
• C. Rogers, William F. Ames, Nonlinear boundary value problems in science and engineering （页面存档备份，存于互联网档案馆）. Academic Press, p. 373, 1989.

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