A Novel Approximate Analytical approach to solve the Boussinesq equation

2020 ◽  
Vol 33 (02) ◽  
Author(s):  
Dr. Amruta Daga Bhandari ◽  
◽  
Dr. Vikas H Pradhan ◽  
Keyword(s):  
Analytical Approach ◽  
Boussinesq Equation

Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

2010 ◽  
Vol 65 (5) ◽  
pp. 411-417 ◽  
Author(s):  
Selin Sarıaydın ◽  
Ahmet Yıldırım
Keyword(s):  
Analytical Approach ◽  
Boussinesq Equation ◽  
Numerical Solutions ◽  
Perturbation Series ◽  
Solitary Wave Solutions ◽  
Convergent Power Series ◽  
Kp Equation ◽  
Homotopy Perturbation ◽  
Wave Solutions ◽  
Petviashvili Equation

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt −uxx−uyy−(u2)xx−uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt −6ux 2 +6uuxx −uxxxx −uyy −uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

The Dynamics of TAT Process

2014 ◽  
Vol 35 (2) ◽  
pp. 103-133 ◽  
Author(s):  
Benoît Verdon ◽  
Catherine Chabert ◽  
Catherine Azoulay ◽  
Michèle Emmanuelli ◽  
Françoise Neau ◽  
...  
Keyword(s):  
Defense Mechanisms ◽  
Analytical Approach ◽  
Therapeutic Process ◽  
Practice Research ◽  
Rorschach Test ◽  
Mental Functioning ◽  
Projective Tests ◽  
The Subject ◽  
Latent Content ◽  
Rigorous Method

After many years of clinical practice, research and the teaching of projective tests, Shentoub and her colleagues (Debray, Brelet, Chabert & al.) put forward an original and rigorous method of analysis and interpretation of the TAT protocols in terms of psychoanalysis and clinical psychopathology. They developed the TAT process theory in order to understand how the subject builds a narrative. Our article will emphasize the source of the analytical approach developed by V. Shentoub in the 1950s to current research; the necessity of marking the boundary between the manifest and latent content in the cards; the procedure for analyzing the narrative, supported by an analysis sheet for understanding the stories' structure and identifying the defense mechanisms; and how developing hypotheses about how the mental functions are organized, as well as their potential psychopathological characteristics; and the formulation of a diagnosis in psychodynamic terms. In conjunction with the analysis and interpretation of the Rorschach test, this approach allows us to develop an overview of the subject's mental functioning, taking into account both the psychopathological elements that may threaten the subject and the potential for a therapeutic process. We will illustrate this by comparing neurotic, borderline, and psychotic personalities.

Maxim Berezovsky C-dur symphony in a context of new biographical scenario of artist’s life-creativity

2018 ◽  
pp. 13-25
Author(s):  
Olha Shumilina
Keyword(s):  
Eighteenth Century ◽  
Instrumental Music ◽  
Analytical Approach ◽  
Spiritual Direction ◽  
Theoretical Research ◽  
Orchestral Music ◽  
Musical Life ◽  
Analysis And Synthesis ◽  
Mental Modeling ◽  
Independent Work

Relevance of the study. The article studies recently found symphony of the prominent Ukrainian composer of the second half of the eighteenth century Maxim Berezovsky. He is widely known now as the author of cyclic spiritual concerts written for the Orthodox worship, and is practically unknown as a musician instrumentalist associated with the imperial theater and the court musical life. The work of M. Berezovsky as a secular musician determined the creative interest in composing instrumental music intended for secular chamber and orchestral music. Main objective of the article is a clarification of M.Berezovsky symphony as one of secular field artworks in the light of new summaries about artist’s life-creativity. Methodology. Taking into account peculiarities of the material and the analytical approach to its study, the methods of theoretical research have been chosen(abstraction, analysis and synthesis, induction and deduction, mental modeling, ascension from abstract to concrete, etc.). Conclusions. As a result of a study the symphony analysis in a context of new authentic statements about M.Berezovsky’s life-creativity. It was stated that this artwork was written not accidentally and detects absolute awareness of the artist in all composer’s niceties – how to build a topic and build a homophonic construction based on it, in a technique of orchestral construction, form creations of that time and etc. From the beginning of his creative career, M. Berezovsky was well aware of the possibilities of the orchestra as a performer, attached to the Italian opera and instrumental music. Symphony enriches our imagination about the works of M. Berezovsky in the field of secular instrumental and operatic music and extends the range of works of the artist beyond the spiritual direction. Some signs indicate that the Symphony was not an independent work, but an overture to the opera Demofont.

Maxim Berezovsky C-dur symphony in a context of new biographical scenario of artist’s life-creativity

2018 ◽  
pp. 13-25
Author(s):  
Olha Shumilina
Keyword(s):  
Eighteenth Century ◽  
Instrumental Music ◽  
Analytical Approach ◽  
Spiritual Direction ◽  
Theoretical Research ◽  
Orchestral Music ◽  
Musical Life ◽  
Analysis And Synthesis ◽  
Mental Modeling ◽  
Independent Work

Relevance of the study. The article studies recently found symphony of the prominent Ukrainian composer of the second half of the eighteenth century Maxim Berezovsky. He is widely known now as the author of cyclic spiritual concerts written for the Orthodox worship, and is practically unknown as a musician instrumentalist associated with the imperial theater and the court musical life. The work of M. Berezovsky as a secular musician determined the creative interest in composing instrumental music intended for secular chamber and orchestral music. Main objective of the article is a clarification of M.Berezovsky symphony as one of secular field artworks in the light of new summaries about artist’s life-creativity. Methodology. Taking into account peculiarities of the material and the analytical approach to its study, the methods of theoretical research have been chosen(abstraction, analysis and synthesis, induction and deduction, mental modeling, ascension from abstract to concrete, etc.). Conclusions. As a result of a study the symphony analysis in a context of new authentic statements about M.Berezovsky’s life-creativity. It was stated that this artwork was written not accidentally and detects absolute awareness of the artist in all composer’s niceties – how to build a topic and build a homophonic construction based on it, in a technique of orchestral construction, form creations of that time and etc. From the beginning of his creative career, M. Berezovsky was well aware of the possibilities of the orchestra as a performer, attached to the Italian opera and instrumental music. Symphony enriches our imagination about the works of M. Berezovsky in the field of secular instrumental and operatic music and extends the range of works of the artist beyond the spiritual direction. Some signs indicate that the Symphony was not an independent work, but an overture to the opera Demofont.

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