Abstract:
An invertible transformation that preserves the class of quasilinear
second-order equations is proposed. Necessary and sufficient
conditions are found under which this transformation carries a quasilinear
equation into an equation with straight characteristics. For
one quasilinear equation the general solution is found by means of
the transformation. Examples of Lagrangians of the form L(u,uxuy) possessing conservation laws of high order are given.
Citation:
F. Kh. Mukminov, “On straightening the characteristics of a quasilinear second-order equation”, TMF, 75:1 (1988), 18–25; Theoret. and Math. Phys., 75:1 (1988), 340–345
This publication is cited in the following 6 articles:
S. Ya. Startsev, “On Bäcklund Transformations Preserving the Darboux Integrability of Hyperbolic Equations”, Lobachevskii J Math, 44:5 (2023), 1929
Ferapontov E.V. Moss J., “Linearly Degenerate Partial Differential Equations and Quadratic Line Complexes”, Commun. Anal. Geom., 23:1 (2015), 91–127
S. I. Svinolupov, V. V. Sokolov, “Factorization of evolution equations”, Russian Math. Surveys, 47:3 (1992), 127–162
L Bombelli, W E Couch, R J Torrence, “Solvable systems of wave equations and non-Abelian Toda lattices”, J. Phys. A: Math. Gen., 25:5 (1992), 1309
E. V. Ferapontov, “Integration of weekly nonlinear semi-hamiltonian systems of hydrodynamic type by methods of the theory of webs”, Math. USSR-Sb., 71:1 (1992), 65–79
V. A. Andreev, “Matrix sine-Gordon equation”, Theoret. and Math. Phys., 84:3 (1990), 920–929