Ansatz’95

References

• Fushchych , W. 1981 . “ 1 Symmetry in problems of mathematical physics ” . In Algebraic – Theortic Studies in Mathematical Physics , 6 – 44 . Kiev : Inst. of Math. Ukrainian Acad. Scie .
   Google Scholar
• Fushchych , W. 1983 . “ On symmetry and exact solutions of some multidimensional equations of mathematical physics problems ” . In Algebraic – Theoretical Methods in Mathematical Physics , 4 – 23 . Kiev : Inst. of Math. Ukrainian Acad. Scie .
   Google Scholar
• Fushchych , W. and Serov , M. 1983 . The symmetry and exact solutions of the nonlinear multi–dimensional Liouville, d’Alembert and eikonal equations . J. Phys. A: Math. Gen. , 16 ( 15 ) : 3645 – 3658 .
   Google Scholar
• Fushchych , W. and Zhdanov , R. 1989 . On some new exact solutions of the nonlinear d’Alembert – Hamilton system . Phys. Lett. , 141A ( 3–4 ) : 113 – 115 .
   Google Scholar
• Fushchych , W. , Zhdanov , R. and Revenko , I. 1991 . General solutions of the nonlinear wave and eikonal equations . Ukrainian Math. J. , 43 ( 11 ) : 1471 – 1486 .
   Google Scholar
• Fushchych , W. , Zhdanov , R. and Yehorchenko , I. 1991 . On the reduction of the nonlinear multi-dimensional wave eqautions and compatibility of the d’Alembert – Hamilton system . J. Math. Anal. Appl. , 161 ( 2 ) : 352 – 360 .
   Google Scholar
• Patera , J. , Winternitz , P. and Zassenhaus , H. 1975 . Continuous subgroups of the fundamental groups of physics . J. Math. Phys. , 16 ( 8 ) : 1597 – 1624 .
   Web of Science ®Google Scholar
• Patera , J. , Winternitz , P. and Zassenhaus , H. 1983 . Maximal abelian subalgebras of real and complex symplectic Lie algebras . J. Math. Phys. , 24 ( 8 ) : 1973 – 1985 .
   Web of Science ®Google Scholar
• Fushchych , W. , Barannyk , A. , Barannyk , L. and Fedorchuk , V. 1985 . Continuous subgroups of the Poincare group P (1, 4) . J. Phys. A: Math. Gen. , 18 ( 5 ) : 2893 – 2899 .
   Google Scholar
• Barannyk , L. and Fushchych , W. 1989 . On continuous subgroups of the generalized Schrödinger groups . J. Math. Phys. , 30 ( 2 ) : 280 – 290 .
   Web of Science ®Google Scholar
• Fushchych , W. , Barannyk , L. and Barannyk , A. 1991 . Subgroup Analysis of the Galilei and Poincare Groups and Reductions of Nonlinear Equations , 300 Kiev : Naukova Dumka .
   Google Scholar
• Clarkson , P. and Kruskal , M. 1989 . New similarity reductions of the Boussinesq equation . J. Math. Phys. , 30 ( 10 ) : 2201 – 2213 .
   Web of Science ®Google Scholar
• Fushchych , W. and Nikitin , A. 1987 . Symmetries of Maxwell’s Equation , 230 Reidel Dordrecht . Russian version 1983, Naukova Dumka 1983
   Google Scholar
• Fushchych , W. 1987 . “ How to extend symmetry of differential equations? ” . In Symmetry and Solutions of Nonlinear Mathematical Physics , 4 – 16 . Kiev : Inst. of Mathem. Ukrainian Acad. Scie .
   Google Scholar
• Fushchych , W. and Tsyfra , I. 1987 . On reduction and solutions of nonlinear wave equations with broken symmetry . J.Phys. A: Math. Gen. , 20 ( 2 ) : 45 – 47 .
   Google Scholar
• Fushchych , W. , Serov , M. and Chopyk , V. 1988 . Conditional invariance and nonlinear heat equations . Dopovidi Ukrainian Acad. Sci. , : 17 – 20 .
   Google Scholar
• Fushchych , W. and Serov , M. 1988 . Conditional invariance and exact solutions of nonlinear acoustic equation . Dopovidi Ukrainian Acad. Sci. , : 27 – 31 .
   Google Scholar
• Fushchych , W. , Shtelen , W. and Serov , M. 1993 . Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics , 430 Kluwer Academic Publishers . (Russian version, 1989, Naukova Dumka)
   Google Scholar
• Fushchych , W. and Shtelen , W. 1983 . On linear and nonlinear systems of differential equations invariant under the Schrödinger group . Theoret. and Math. Fisika , 56 ( 3 ) : 387 – 394 .
   Google Scholar
• Ovsyannikov , L. 1978 . Group Analysis of Differential Equations , Moskow : Nauka .
   Google Scholar
• Dorodnyzyn , W. , Knyazeva , I. and Svirshchevski , S. 1983 . Group properties of the heat equation with a source in two and three dimensions . Defferentsial’nye Uravneniya , 19 ( 7 ) : 1215 – 1224 .
   Google Scholar
• Fushchych , W. and Serov , M. 1990 . Conditional symmetry and reduction of nonlinear heat equation . Dopovidi Ukrainian Acad. Sci. , : 24 – 28 .
   Google Scholar
• Serov , M. 1990 . Conditional invariance and exact solutions of nonlinear heat equation . Ukrainian Math. Journal , 42 ( 10 ) : 1370 – 1376 .
   Google Scholar
• Clarkson , P. and Mansfield , E. 1995 . Algorithms for the nonclassical method of symmetryreductions . SIAM J. Appb. Math. ,
   Google Scholar
• Fushchych , W. 1991 . Conditional symmetry of the equations of mathematical physics . Ukrainian Math. J. , 43 ( 1 ) : 1456 – 1470 .
   Google Scholar
• Fushchych , W. and Myronyuk , P. 1991 . Conditional symmetry and exact solutions of nonlinear acoustics equation . Dopovidi of the Ukrainian Acad. Sciences , : 23 – 26 .
   Google Scholar
• Fushchych , W. and Repeta , V. 1991 . Exact solutions of equations of gas dynamics and nonlinear acoustics . Dopovidi of the Ukrainian Acad. Sciences , : 35 – 38 .
   Google Scholar
• Fushchych , W. and Seheda , Yu. 1977 . On a new invariance algebra for the free Schrödinger equation . Doklady Acad. sci. USSR , 232 ( 4 ) : 800 – 801 .
   Google Scholar
• Fushchych , W. and Nikitin , A. 1994 . Symmetries of Equations of Quantum Mechanics , 500 Allerton Press . (in Russian 1990, Moscow, Nauka)
   Google Scholar
• Fushchych , W. 1971 . On additional invariance of relativistic equations of motion . Teoretich. and Matem. Fizika , 7 ( 1 ) : 3 – 12 .
   Google Scholar
• Fushchych , W. 1974 . On additional invariance of the Dirac and Maxwell equations . Lettere Nuovo Cimento , 11 ( 10 ) : 508 – 512 .
   Google Scholar
• Fushchych , W. 1976 . On additional invariance of the Klein–Gordon–Fock equation . Dokl. Acad. Sci. USSR , 230 ( 3 ) : 570 – 573 .
   Google Scholar
• Fushchych , W. and Zhdanov , R. 1994 . Antireduction and exact solutions of nonlinear heat equation . J. Nonlinear Math. Phys. , 1 ( 1 ) : 60 – 64 .
   Google Scholar
• Fushchych , W. 1992 . New nonlinear equations for electromagnetic field having the velocity different from c . Dopovidi of the Ukrainian Academy of Sciences , : 24 – 28 .
   Google Scholar
• Fushchych ≡ Fushchich.
   Google Scholar