The composers who wrote the most sucessful sonatas for cello and piano were Beethoven and Brahms. Other composers have written examples also, but for many it was a one-time endeavor. Alkan wrote only one, as did his friend and sometime neighbor, Chopin.
As with most of Alkan's music, the technical (and musical) difficulties of the cello sonata are many for both instruments, not least of all keeping the proper balance between the two. It is in 4 movements, with each movement being in a differet key:
I. Allegro molto - This movement isi n the home key of E major and begins straight away with a theme, the first of three main themes of the exposition, although there is much of the material that connects the main themes that can be thought of as short secondary theme material. (The recording that I've linked to at the end of this article does not take the exposition repeat, which in my opinion is somewhat excusable in music that is more familiar, but in works that are heard but seldom, it would help the listener find their way a little better if the themes were placed in the ear more securely by a repitition of them.) The development section is extensive and begins with the development of the short pizacatto motive that ends the exposition along with other material. The first theme appears, plays for a few bars before going off in different keys. Other themes follow suit. The recapitulation proper begins with the first theme followed by other material from the exposition that has modulated to other keys. In a short coda that is marked brilliante, the movement ends.
II. Allegrettino - This movement is in A-flat major. In contrast to the opening movement, this has the feeling of a gently swaying dance, but there are surprises as minor keys float into the mix giving a feeling of unrest to the middle section.
III. Adagio - This movement is in C major. Alkan was devoutly Jewish and an Old Testement scholar. He prefaced the music with a quotation from the Old Testement book of Micah:
"As dew from the Lord how the Jewish people endure, awaiting help from God alone."The movement begins with three-note motives on the cello followed by a harmonic as the piano lags slightly behind as it plays its own three-note motive. The music is mysterious, not least of all for the incessant pizacatto notes played in a seemingly random pattern by the cello as the piano gently plays sixteenth notes in both hands in the treble topped by a melody even higher in the right hand. The music reaches ever higher until it comes to rest with a high C major chord in the piano while the cello plays a low C pizacatto.
IV. Finale alla Salterella - Prestissimo - A dance in the key of E minor that gets wilder and wilder as it goes. It's full of dotted rhythms and extremes in range of both instruments until a trill in both hands of the piano along with an arpeggiated chord in the cello lead to the final chord.