Nonclassical Potential Symmetries and New Explicit Solutions of the Burgers Equation

Abstract

Unlike chlorination fluorination of ammine complexes of platinum(IV) in aqueous solution does not lead to haloamido complexes. Instead, the triammine complexes [Pt(NH3)3Cl3]Cl and [Pt(NH3)3(NCl2)2Cl]Cl yield no definite main product, and the tetrammine and pentammine complexes trans-[Pt(NH3)4C12]C12, [Pt(NH3)4(NCl2)Cl]Cl2, [Pt(NH3)5Cl]Cl3, and [Pt(NH3)5(OH)]Cl3 form the sparingly soluble complex trans -[Pt (NH3 )4C12] (H2F3 )2 • 2 H-20 as the main product.

New explicit solutions of the Burgers equation

“…Now we need to solve for the coefficient functions τ, ξ, φ and η from (9). Although Equation (9) are too complicated to solve in general, some special solutions can be derived.…”

“…Since we have two more expressions ξ and ξ than paper Gandarias [8], we can obtain a few more non-classical potential symmetries accordingly here. Using three typical nonclassical potential symmetry generators of (15), we obtained many explicit solutions in Qin [9]. Many new explicit solutions are constructed by using three special nonclassical potential symmetry generators of (16) in another paper.…”

“…A few new explicit solutions of the Burgers equation are obtained by using its nonclassical potential symmetry group in Gandarias [8]. Several new explicit solutions of the Burgers equation have been obtained by using its typical nonclassical potential symmetry generators in Qin [9]. Further study reveals these explicit solutions obtained in Qin [9] are only special cases of general ones.…”

“…Several new explicit solutions of the Burgers equation have been obtained by using its typical nonclassical potential symmetry generators in Qin [9]. Further study reveals these explicit solutions obtained in Qin [9] are only special cases of general ones. In this paper, several previously unknown explicit solutions of the Burgers equation are obtained by applying the nonclassical Lie group method to the associated equivalent system.…”

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Many new and valuable explicit solutions of the Burgers equation are constructed by using three typical nonclassical potential symmetry generators of Burgers equation in [9]. In fact, most of these solutions cannot be derived from the Lie symmetry group of Burgers or its adjoined equation, nor through the Hopf-Cole transformation from the heat equation.

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