English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The symmetry reduction of the equation (1) was considered in [1–5]. Maximal subalgebras of rank n of the algebra AP (1, n) were described in [3, 4]. These results allow to construct all symmetry ansatzes reducing the equation (1) to ordinary differential equations. Using the solutions of the reduced equations, some classes of multiparametric exact solutions of the equation (1) were found. Classification of the maximal subalgebras of rank n − 1 of the algebra AP (1, n) was given in [5]. Using these subalgebras ansatzes reducing equation (1) to equations of two variables were constructed. The present paper continues the research which was carried out in [3–5]. Here new operators of conditional symmetry of the d’Alembert equation are found. Using these operators conditionally-invariant ansatzes reducing equation (1) to ordinary differential equations are built. New classes of exact solutions of this equation are constructed. Consider the subalgebra L = where Ga = J0a − Jam, a = 1, 2, . . . ,m− 1. Let solutions of the equation (1) satisfy the conditions G1u = 0, . . . , Gm−1u = 0, Pm+1u = 0, . . . , Pnu = 0. (2)

Conditional Symmetry and Exact Solutions of the Multidimensional Nonlinear d'Alembert Equation