The method of construction the Lax-Zakharove-Shabat pseudo-representations and representations of a nonlinear partial differential equations which allowed the conjugative equation with standard definition was found. This method was based on a using the general Lagrange identities. In particular the new multi-component nonlinear PDE sets which allowed a multi-soliton solutions was found. The method of construction an exact solutions of Liouville equation in multi-dimension space was found. This solutions functionality connects with the n-form defined on the one argument vector-function space. The analogical solutions of the multi-dimension Toda-chains was found too. The new class of nonlinear auto-wave model processes in diffusion media (diffusion Toda-chains) was found. This models allow the exact solution with the arbitrary functional parameters. The analogical class of the nonlinear auto-wave model was found for the systems which described by nonlinear telegraph equations. In a frame of this work the new special superposition principe of simple solution of the nonlinear diffusion equation $u_t=D\Delta \log u +\lambda u$ and nonlinear telegraph equation $u_t=D(\partial^2_t-\partial^2_x) \log u +\lambda u$ was found. A number of papers (with Chervon S.V. and Shchigolev V.K.) were devoted to the cosmological models which unified the all stages of Universe evolution (global evolution) with many form of matter: perfect fluid, scalar field, Yang–Mills fields.
Main publications:
Zhuravlev V. M. O novom predstavlenii dvumernykh uravnenii dinamiki neszhimaemoi zhidkosti // Prikladnaya matematika i mekhanika, 1994, 58 (6), 61–67.
Zhuravlev V. M. Modeli nelineinykh volnovykh protsessov, dopuskayuschie solitonnye resheniya // ZhETF, 1996, 110 (6), 910–929.
Zhuravlev V. M. Tochnye resheniya uravnenii Liuvillya v mnogomernykh prostranstvakh // TMF, 1999, 120 (1), 3–19.
Zhuravlev V. M. Tochnye resheniya uravnenii nelineinoi diffuzii $u_t-D\Delta \log u -\lambda u= 0$ v dvumernom koordinatnom prostranstve // TMF, 2000, 124 (2), 265–278.
Zhuravlev V. M. Dvukhkomponentnye kosmologicheskie modeli s peremennym uravneniem sostoyaniya veschestva i teplovym ravnovesiem komponent // ZhETF, 2001, 120 (5), 1043–1061.
